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#### Annotation 1409645939980

 #aviation #wiki An airplane or aeroplane (informally plane) is a powered , fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller .

Airplane - Wikipedia
magelink] [emptylink] The first flight of an airplane, the Wright Flyer on December 17, 1903 [imagelink] [emptylink] An All Nippon Airways Boeing 777 -300 taking off from New York JFK Airport . <span>An airplane or aeroplane (informally plane) is a powered , fixed-wing aircraft that is propelled forward by thrust from a jet engine , propeller or rocket engine . Airplanes come in a variety of sizes, shapes, and wing configurations . The broad spectrum of uses for airplanes includes recreation , transportation of goods and people, military , and

#### Flashcard 1409649085708

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#aviation #wiki
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An airplane or aeroplane (informally plane) is a powered , fixed-wing aircraft that is propelled forward by thrust from a [...] or propeller .
jet engine

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An airplane or aeroplane A (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller.

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Airplane - Wikipedia
her uses, see Airplane (disambiguation) and Aeroplane (disambiguation). [imagelink] North American P-51 Mustang, a World War II fighter [imagelink] The first flight of an airplane, the Wright Flyer on December 17, 1903 <span>An airplane or aeroplane A (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, transportation of goods and people, military, and re

#### Flashcard 1409650134284

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#aviation #wiki
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An airplane or aeroplane (informally plane) is a powered , fixed-wing aircraft that is propelled forward by thrust from a jet engine or [...] .
propeller

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An airplane or aeroplane A (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller.

#### Original toplevel document

Airplane - Wikipedia
her uses, see Airplane (disambiguation) and Aeroplane (disambiguation). [imagelink] North American P-51 Mustang, a World War II fighter [imagelink] The first flight of an airplane, the Wright Flyer on December 17, 1903 <span>An airplane or aeroplane A (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, transportation of goods and people, military, and re

#### Flashcard 1428269960460

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#algebra-baldor
Question
El camino recorrido a la derecha o hacia arriba de un punto se desig na con el signo [...] y el camino recorrido a la izquierda o hacia abajo de un punto se representa con el signo [...] .
+

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El camino recorrido a la derecha o hacia arriba de un punto se desig na con el signo + y el camino recorrido a la izquierda o hacia abajo de un punto se representa con el signo —.

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#### Flashcard 1442143931660

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#analyst-notes #cfa-level-1 #corporate-finance #reading-35-capital-budgeting #study-session-10
Question
Assumptions of capital budgeting are:

• Capital budgeting decisions must be based on cash flows, not accounting income.

• Cash flow timing is critical.

• The opportunity cost should be charged against a project.

• Expected future cash flows must be measured on an after-tax basis.

• [...]
Ignore how the project is financed.

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is on hand does not mean it's free. See below for the definition of opportunity cost. Expected future cash flows must be measured on an after-tax basis. The firm's wealth depends on its usable after-tax funds. <span>Ignore how the project is financed. Interest payments should not be included in the estimated cash flows since the effects of debt financing are reflected in the cost of capital used to discount the cash flows. The existe

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Subject 2. Basic Principles of Capital Budgeting
Capital budgeting decisions are based on incremental after-tax cash flows discounted at the opportunity cost of capital. Assumptions of capital budgeting are: Capital budgeting decisions must be based on cash flows, not accounting income. Accounting profits only measure the return on the invested capital. Accounting income calculations reflect non-cash items and ignore the time value of money. They are important for some purposes, but for capital budgeting, cash flows are what are relevant. Economic income is an investment's after-tax cash flow plus the change in the market value. Financing costs are ignored in computing economic income. Cash flow timing is critical because money is worth more the sooner you get it. Also, firms must have adequate cash flow to meet maturing obligations. The opportunity cost should be charged against a project. Remember that just because something is on hand does not mean it's free. See below for the definition of opportunity cost. Expected future cash flows must be measured on an after-tax basis. The firm's wealth depends on its usable after-tax funds. Ignore how the project is financed. Interest payments should not be included in the estimated cash flows since the effects of debt financing are reflected in the cost of capital used to discount the cash flows. The existence of a project depends on business factors, not financing. Important capital budgeting concepts: A sunk cost is a cash outlay that has already been incurred and which

#### Flashcard 1479599328524

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#aviation #wiki
Question
An airplane or aeroplane (informally [...]) is a powered , fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller .
plane

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An airplane or aeroplane (informally plane) is a powered , fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller .

#### Original toplevel document

Airplane - Wikipedia
sambiguation) and Aeroplane (disambiguation). [imagelink] [emptylink] North American P-51 Mustang, a World War II fighter [imagelink] [emptylink] The first flight of an airplane, the Wright Flyer on December 17, 1903 <span>An airplane or aeroplane (informally plane) is a powered, fixed-wing aircraft that is propelled forward by thrust from a jet engine or propeller. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, transportation of goods and people, military, and re

#### Flashcard 1730169408780

Question
EP uses an iterative approach that leverages [...] of the target distribution.
the factorization structure

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EP finds approximations to a probability distribution. It uses an iterative approach that leverages the factorization structure of the target distribution.

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Expectation propagation - Wikipedia
Expectation propagation From Wikipedia, the free encyclopedia Jump to: navigation, search Expectation propagation (EP) is a technique in Bayesian machine learning. <span>EP finds approximations to a probability distribution. It uses an iterative approach that leverages the factorization structure of the target distribution. It differs from other Bayesian approximation approaches such as Variational Bayesian methods. References[edit source] Thomas Minka (August 2–5, 2001). "Expectation Propagation

#### Flashcard 1731460205836

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#matrix
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a square matrix A is called diagonalizable if it is similar to [...]

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In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1 AP is a diagonal matrix.

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Diagonalizable matrix - Wikipedia

#### Flashcard 1731639774476

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#linear-algebra
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a linear map is a mapping VW that preserves the operations of [...].

addition and scalar multiplication

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thematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of <span>addition and scalar multiplication. <span><body><html>

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Linear map - Wikipedia
Linear operator) Jump to: navigation, search "Linear transformation" redirects here. For fractional linear transformations, see Möbius transformation. Not to be confused with linear function. <span>In mathematics, a linear map (also called a linear mapping, linear transformation or, in some contexts, linear function) is a mapping V → W between two modules (including vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication. An important special case is when V = W, in which case the map is called a linear operator, [1] or an endomorphism of V. Sometimes the term linear function has the same meaning as li

#### Flashcard 1731665202444

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#dynamic-programming
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memoization saves [...] by storing the results of expensive function calls and returning the cached result when the same inputs occur again.
computational time

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In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again.

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Memoization - Wikipedia
dia, the free encyclopedia Jump to: navigation, search Not to be confused with Memorization. "Tabling" redirects here. For the parliamentary procedure, see Table (parliamentary procedure). <span>In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing [1] . Although related to caching, memoi

#### Flashcard 1731674901772

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#dynamic-programming
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dynamic programming aims to solve each subproblems [...] and storing their solutions.
just once

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ter science, mathematics, management science, economics and bioinformatics, dynamic programming (also known as dynamic optimization) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, <span>solving each of those subproblems just once, and storing their solutions. The next time the same subproblem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving c

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Dynamic programming - Wikipedia
This article's factual accuracy is disputed. Relevant discussion may be found on the talk page. Please help to ensure that disputed statements are reliably sourced. (November 2015) (Learn how and when to remove this template message) <span>In computer science, mathematics, management science, economics and bioinformatics, dynamic programming (also known as dynamic optimization) is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions. The next time the same subproblem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time at the expense of a (hopefully) modest expenditure in storage space. (Each of the subproblem solutions is indexed in some way, typically based on the values of its input parameters, so as to facilitate its lookup.) The technique of storing solutions to subproblems instead of recomputing them is called "memoization". Dynamic programming algorithms are often used for optimization. A dyna

#### Flashcard 1731723398412

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#stochastics
Question
In a martingale, the expectation of the next value in the sequence equals to [...]
the present observed value

even given knowledge of all prior observed values.

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In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values. <body><html>

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Martingale (probability theory) - Wikipedia
h For the martingale betting strategy, see martingale (betting system). [imagelink] Stopped Brownian motion is an example of a martingale. It can model an even coin-toss betting game with the possibility of bankruptcy. <span>In probability theory, a martingale is a sequence of random variables (i.e., a stochastic process) for which, at a particular time in the realized sequence, the expectation of the next value in the sequence is equal to the present observed value even given knowledge of all prior observed values. Contents [hide] 1 History 2 Definitions 2.1 Martingale sequences with respect to another sequence 2.2 General definition 3 Examples of martingales 4 Submartingales, super

#### Flashcard 1735977733388

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#stochastics
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interpreted as a random element in a function space, a stochastic process can also be called a [...]
random function

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The term random function is also used to refer to a stochastic or random process, [25] [26] because a stochastic process can also be interpreted as a random element in a function space. <

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Stochastic process - Wikipedia
are considered the most important and central in the theory of stochastic processes, [1] [4] [23] and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries. [21] [24] <span>The term random function is also used to refer to a stochastic or random process, [25] [26] because a stochastic process can also be interpreted as a random element in a function space. [27] [28] The terms stochastic process and random process are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. [27] [29]

#### Flashcard 1737364213004

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functional programming avoids [...]
changing-state and mutable data

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span> In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids <span>changing-state and mutable data <span><body><html>

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Functional programming - Wikipedia
ithic) Object-oriented Actor-based Class-based Concurrent Prototype-based By separation of concerns: Aspect-oriented Role-oriented Subject-oriented Recursive Value-level (contrast: Function-level) Quantum programming v t e <span>In computer science, functional programming is a programming paradigm—a style of building the structure and elements of computer programs—that treats computation as the evaluation of mathematical functions and avoids changing-state and mutable data. It is a declarative programming paradigm, which means programming is done with expressions [1] or declarations [2] instead of statements. In functional code, the output value of a fu

#### Flashcard 1741142494476

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#measure-theory #stochastics
Question
The smallest sigma-algebra is [...].
{∅, Ω}

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The smallest sigma-algebra is {∅, Ω}. It must contain Ω by definition, and it must contain ∅ because it is Ω c . Unions and intersections of Ω and ∅ give us the same sets back, no new sets.

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#### Flashcard 1741151931660

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#measure-theory #stochastics
Question
the elements of a sigma-algebra $$\mathcal{A}$$ are called [...].
measurable sets

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A set Ω equipped with a sigma-algebra is called a measurable space and usually denoted as a pair . In this context, the elements of are called measurable sets.

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#### Flashcard 1741240536332

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#poisson-process #stochastics
Question
In a homogeneous Poisson point process with , is [...] and is [...]
Lebegues measure, constant

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If a Poisson point process has a parameter of the form , where is Lebegues measure, and is a constant, then the point process is called a homogeneous or stationary Poisson point process.

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Poisson point process - Wikipedia
edit source] For all the different settings of the Poisson point process, the two key properties [b] of the Poisson distribution and complete independence play an important role. [25] [45] Homogeneous Poisson point process[edit source] <span>If a Poisson point process has a parameter of the form Λ = ν λ {\displaystyle \textstyle \Lambda =\nu \lambda } , where ν {\displaystyle \textstyle \nu } is Lebegues measure, which assigns length, area, or volume to sets, and λ {\displaystyle \textstyle \lambda } is a constant, then the point process is called a homogeneous or stationary Poisson point process. The parameter, called rate or intensity, is related to the expected (or average) number of Poisson points existing in some bounded region, [49] [50] where rate is usually used when the

#### Flashcard 1744165539084

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#lebesgue-integration
Question
the Banach-Tarski paradox suggests that picking out [...] is an essential prerequisite.
a suitable class of measurable subsets

The choice of unmeasurable sets can lead to the Banach-Tarski paradox

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er set theory developments showed (see non-measurable set), it is actually impossible to assign a length to all subsets of ℝ in a way that preserves some natural additivity and translation invariance properties. This suggests that picking out <span>a suitable class of measurable subsets is an essential prerequisite. <span><body><html>

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Lebesgue integration - Wikipedia
a useful abstraction of the notion of length of subsets of the real line—and, more generally, area and volume of subsets of Euclidean spaces. In particular, it provided a systematic answer to the question of which subsets of ℝ have a length. <span>As later set theory developments showed (see non-measurable set), it is actually impossible to assign a length to all subsets of ℝ in a way that preserves some natural additivity and translation invariance properties. This suggests that picking out a suitable class of measurable subsets is an essential prerequisite. The Riemann integral uses the notion of length explicitly. Indeed, the element of calculation for the Riemann integral is the rectangle [a, b] × [c, d], whose area is calculated to be

#### Flashcard 1744236317964

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#lebesgue-integration
Question
the domain of integration in Lebesgue integration is defined as a [...]
set

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A technical issue in Lebesgue integration is that the domain of integration is defined as a set (a subset of a measure space), with no notion of orientation.

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Lebesgue integration - Wikipedia
1 ] ) = 0 , {\displaystyle \int _{[0,1]}1_{\mathbf {Q} }\,\mathrm {d} \mu =\mu (\mathbf {Q} \cap [0,1])=0,} because Q is countable. Domain of integration[edit source] <span>A technical issue in Lebesgue integration is that the domain of integration is defined as a set (a subset of a measure space), with no notion of orientation. In elementary calculus, one defines integration with respect to an orientation: ∫ b a

#### Flashcard 1744237890828

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#lebesgue-integration
Question
the domain of integration in Lebesgue integration has no notion of [...].
orientation

Is this why positive and negative part are dealt with separately?

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A technical issue in Lebesgue integration is that the domain of integration is defined as a set (a subset of a measure space), with no notion of orientation.

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Lebesgue integration - Wikipedia
1 ] ) = 0 , {\displaystyle \int _{[0,1]}1_{\mathbf {Q} }\,\mathrm {d} \mu =\mu (\mathbf {Q} \cap [0,1])=0,} because Q is countable. Domain of integration[edit source] <span>A technical issue in Lebesgue integration is that the domain of integration is defined as a set (a subset of a measure space), with no notion of orientation. In elementary calculus, one defines integration with respect to an orientation: ∫ b a

#### Flashcard 1744254930188

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#linear-algebra
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the cross product is [...123...].

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In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane

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Cross product - Wikipedia
edia, the free encyclopedia Jump to: navigation, search This article is about the cross product of two vectors in three-dimensional Euclidean space. For other uses, see Cross product (disambiguation). <span>In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space (R 3 ) and is denoted by the symbol ×. Given two linearly independent vectors a and b, the cross product, a × b, is a vector that is perpendicular to both a and b and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product). If two vectors have the same

#### Flashcard 1744294251788

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#lebesgue-integration
Question

To assign a value to [...], the only reasonable choice is to set:

the integral of the indicator function 1S of a measurable set S consistent with the given measure μ

Notice that the result may be equal to +∞ , unless μ is a finite measure.
Trick: just read the expression from left to right

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To assign a value to the integral of the indicator function 1 S of a measurable set S consistent with the given measure μ, the only reasonable choice is to set: Notice that the result may be equal to +∞ , unless μ is a finite measure.

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Lebesgue integration - Wikipedia
x ) {\displaystyle \int _{E}f\,\mathrm {d} \mu =\int _{E}f\left(x\right)\,\mathrm {d} \mu \left(x\right)} for measurable real-valued functions f defined on E in stages: Indicator functions: <span>To assign a value to the integral of the indicator function 1 S of a measurable set S consistent with the given measure μ, the only reasonable choice is to set: ∫ 1 S d μ = μ ( S ) . {\displaystyle \int 1_{S}\,\mathrm {d} \mu =\mu (S).} Notice that the result may be equal to +∞, unless μ is a finite measure. Simple functions: A finite linear combination of indicator functions ∑ k a

#### Flashcard 1748756204812

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#borel-algebra #measure-theory
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any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on [...].
all Borel sets of that space

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Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space.

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Borel set - Wikipedia
or a topological space X, the collection of all Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets (or, equivalently, all closed sets). <span>Borel sets are important in measure theory, since any measure defined on the open sets of a space, or on the closed sets of a space, must also be defined on all Borel sets of that space. Any measure defined on the Borel sets is called a Borel measure. Borel sets and the associated Borel hierarchy also play a fundamental role in descriptive set theory. In some contexts

#### Flashcard 1748768525580

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#measure-theory #probability-measure
Question
if you know what a probability measure does on [...], then you know what it does on all the Borel sets.
every interval

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One thing that makes the Borel sets so powerful is that if you know what a probability measure does on every interval, then you know what it does on all the Borel sets.

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#### Flashcard 1748770622732

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#measure-theory #probability-measure
Question
if you know what a probability measure does on every interval, then you know what it does on [...].
all the Borel sets

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One thing that makes the Borel sets so powerful is that if you know what a probability measure does on every interval, then you know what it does on all the Borel sets.

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A Hilbert space is an abstract vector space possessing the structure of [...] that allows length and angle to be measured.

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A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured.

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Hilbert space - Wikipedia
e state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space. <span>The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point o

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#matrix-decomposition
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By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an [...]

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By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an eigenbasis

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Matrix (mathematics) - Wikipedia
x. In complex matrices, symmetry is often replaced by the concept of Hermitian matrices, which satisfy A ∗ = A, where the star or asterisk denotes the conjugate transpose of the matrix, that is, the transpose of the complex conjugate of A. <span>By the spectral theorem, real symmetric matrices and complex Hermitian matrices have an eigenbasis; that is, every vector is expressible as a linear combination of eigenvectors. In both cases, all eigenvalues are real. [29] This theorem can be generalized to infinite-dimensional situations related to matrices with infinitely many rows and columns, see below. Invertible matrix and its inverse[edit s

#### Annotation 1752698326284

 #inner-product-space In a normed space, the statement of the parallelogram law is an equation relating norms:

Parallelogram law - Wikipedia
2 {\displaystyle BD^{2}+AC^{2}=2a^{2}+2b^{2}} Q.E.D. The parallelogram law in inner product spaces[edit source] [imagelink] Vectors involved in the parallelogram law. <span>In a normed space, the statement of the parallelogram law is an equation relating norms: 2 ‖ x ‖ 2 + 2 ‖ y ‖

#### Flashcard 1752701472012

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#inner-product-space
Question
In a normed space, the statement of the parallelogram law is [...]:
an equation relating norms

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In a normed space, the statement of the parallelogram law is an equation relating norms:

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Parallelogram law - Wikipedia
2 {\displaystyle BD^{2}+AC^{2}=2a^{2}+2b^{2}} Q.E.D. The parallelogram law in inner product spaces[edit source] [imagelink] Vectors involved in the parallelogram law. <span>In a normed space, the statement of the parallelogram law is an equation relating norms: 2 ‖ x ‖ 2 + 2 ‖ y ‖

#### Flashcard 1753096785164

Question
A question about confidence regarding what you do;
What would it take for you to be confident that we'll meet your requirements?

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#### Flashcard 1753099144460

Question
Confirm what they want.
most of the work on the ...... will be done on..... Is that what you want?

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Question
A time question.
How much time would we have to prepare ....?

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Question
You can do what they want, ask for some commitments?
We won't have any problem with the ...... Are you ready to make some commitments?

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Question
When you ask about commitments and they ask; What do you mean? Say;
I'm ready to make some commitments if you are.

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#### Flashcard 1753111203084

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If prospect makes a comment, ask;
Is that something y ou want to talk about now?

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Question
What are some good questions to ask to make certain that you have uncovered everything that is important to the prospect regarding your discussion?
Is there anything else we should discuss? Are you satisfied we've covered all of your concerns?

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#### Flashcard 1753115921676

Question
What is a good action confirming question?
Are you sure this is what you want to do?

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Are you willing to release the order to us tomorrow?

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Question
I'll need the Purchasing Manager's signature on the first order because it's so large, and because we're depending on you for a critical delivery schedule.
Will the Purchasing Manager be in tomorrow?

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#### Flashcard 1753122999564

Question
A confirming question about any additional information that should be added to the issue at hand?
Is there anything else we should know or discuss today about the (the issue at hand)...?

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#### Flashcard 1753126145292

Question
Thanks for your prompt attention.
VP: You're welcome.

status measured difficulty not learned 37% [default] 0

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#### Flashcard 1753128504588

Question
Asking about future opportunity to work them;
Will we have the opportunity to work with you on,,,, when the time is right?

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#### Annotation 1753132698892

 High Probability Selling teaches that selling is the art of Agreement and Commitment. Only High Probability Prospects - those who are willing to commit step-by-step to the buying process - are worth the salesperson's time, energy and resources.

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#### Annotation 1753134533900

 In High Probability Selling, the basic idea is to disqualify prospects who don't fit certain criteria, and that can happen at any point in the process

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#### Annotation 1753137941772

 Selling is reaching a series of agreements with those prospects who first acknowledge that they need, want and can afford what we're selling, and commit to buy from us at a specified time if we fulfill their Conditions of Satisfaction.

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#### Annotation 1753139776780

 What most salespeople don't realize is they're wasting a lot of good selling opportunities by seeing too many of the wrong prospects. That wastes time, talent, energy, emotional strength and company resources

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#### Flashcard 1753143184652

Question
How do you know whether you have a good prospect?
Here's how we categorize them: 1. Some prospects already need, want, and can afford what we sell. That group is happy to buy from us. 2. Some prospects need and can afford what we sell but do not want it. 3. Some prospects need and want what we sell but can't afford it. 4. Some prospects need, want and can afford what we sell, but won't buy from us. Like prospects who want what we sell, but prefer another brand or source. Obviously, we should be spending most of our time and resources talking to prospects in category one.

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#### Annotation 1753145543948

 How do you know whether you have a good prospect? Here's how we categorize them: 1. Some prospects already need, want, and can afford what we sell. That group is happy to buy from us. 2. Some prospects need and can afford what we sell but do not want it. 3. Some prospects need and want what we sell but can't afford it. 4. Some prospects need, want and can afford what we sell, but won't buy from us. Like prospects who want what we sell, but prefer another brand or source. Obviously, we should be spending most of our time and resources talking to prospects in category one.

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#### Annotation 1753147903244

 Most prospects make up their minds about an offer in the first minute. That's about all the time worth spending when you're prospecting.

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#### Annotation 1753149476108

 Aggressive salespeople create defensive prospects. Persistence breeds annoyance. Those approaches and other things salespeople do to manipulate prospects in order to get an appointment are what cause "sales resistance."

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#### Annotation 1753151048972

 Millions of people were taught sales techniques based on a model that most salespeople found difficult to learn and uncomfortable to apply. This technology was based on the idea that you could use psychology to make almost anyone buy almost anything.

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#### Annotation 1753153408268

 We've discovered that what works in sales is very different from what we were taught traditionally. And what we've learned fits into a pattern that is governed by certain basic principles, which is why High Probability Selling is called a technology.

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#### Annotation 1753155767564

 Some sales systems tell you to keep asking for the order until the prospect throws you out. We never ask for the order.

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#### Annotation 1753158126860

 We don't waste time trying to sell prospects who probably won't buy from us. Why waste the effort?

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#### Annotation 1753159699724

 It's better to be seeing five High Probability Prospects, who've already told you that they need, want and can afford what you're selling and will buy from you now if you can meet certain criteria?

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#### Annotation 1753163631884

 You have to eliminate sales resistance in the prospects you contact.

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#### Annotation 1753165991180

 We don't handle objections. In a High Probability Selling environment, the prospect is involved in the process of reaching agreement with you, not trying to resist being convinced. "Objections" don't surface as arguments or reasons why the prospect won't buy. They surface as points that have to be addressed, discussed and negotiated

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#### Annotation 1753167564044

 With the five-step model - Attention, Interest, Desire, Conviction, and Action (Closing), the whole approach is very manipulative and adversarial. It also takes a lot of time, a lot of energy and a ton of practice. It's also difficult to do without offending the prospect. And what's most offensive to prospects is that the salesperson does almost all of the talking. In this play, the customer's only role is answering yes to rhetorical questions.

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#### Annotation 1753169923340

 Attention If you have to do something unusual to get a prospect's attention, you don't have a very good prospect; certainly not a High Probability Prospect. Disqualifying a prospect like that prevents you from wasting your time. When you're offering people something they want, they naturally pay attention.

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#### Annotation 1753171496204

 Interest A lot of time is wasted trying to get uninterested people interested, and in boring people who are already interested. More importantly, there are a lot of interested people who won't act. The prospect's level of interest is meaningless. What counts is whether your prospect wants what you have to sell.

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#### Annotation 1753173069068

 Desire Rather than creating desire for your product or service by telling prospects about its features and benefits, you should be showing them how your product satisfies the desires they already have. But that should only be done after they've made a conditional commitment to buy.

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#### Annotation 1753174641932

 Conviction By the time you get to this step, you're in the "Can You Top This" mode. While you're showing, telling and proving, the prospect has yet to either set the limits for his satisfaction or make any commitment.

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#### Annotation 1753176214796

 Action If you don't close until the end of your presentation you've put out too much effort for an uncertain result. That invites crushing disappointment. In High Probability Selling, the entire process is the close.

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#### Annotation 1753178574092

 Learning High Probability Selling requires effort and lots of practice. But once you learn it, selling becomes easier and more natural and you'll increase your sales. And it's not a matter of concentration. Once you learn it, you own it. It becomes part of you.

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#### Annotation 1753180933388

 If you want to sell as many prospects as you can within the time you have available, it's much more efficient to start with prospects who already want your product or service. With that in mind, we skip the first four steps and begin with the "Action" (close) step. That's where you want a prospect's attention. But, we don't use traditional closing techniques. We have too much respect for people to manipulate them. After you learn more about High Probability Prospecting, you'll see that we're always closing.

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#### Annotation 1753182506252

 High Probability Selling is a totally different approach. Traditional selling does try to get the prospect to do something, whether he wants to or not. Our object is to determine whether you and the prospect have a mutually beneficial basis for doing business, and if not, to go your separate ways. If there isn't mutual agreement and mutual commitment at any point in the discussion, the process stops. We continuously give the prospect every opportunity to disqualify himself, early and often, from beginning to end. As a result, if you and the prospect get through the three phases of the process, there's a very high level of assurance that both of you will get the result that you each want.

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#### Annotation 1753184865548

 The three phases of High Probability Selling are: High Probability Prospecting High Probability Selling High Probability Closing

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#### Annotation 1753187224844

 In High Probability Selling, I think you'll decide that it's worthwhile to give up the struggle and save the effort and frustration.

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#### Annotation 1753190370572

 High Probability Selling will make a difference in your career. Your commissions really take off. You will be more relaxed at work and feel better about yourself, have more dignity and self-esteem, and be more in control of the selling process.

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#### Annotation 1753192729868

 You are correct in not using the company's resources in a no-win activity. Most prospects respect that kind of no-nonsense approach.

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#### Annotation 1753195089164

 If the prospect shows an unwillingness to have a frank and open discussion end the meeting.

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#### Annotation 1753197448460

 There is a value in questions and a value in not going forward when you don't get clear and honest answers to them.

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#### Annotation 1753199807756

 High Probability Selling is really a method of inquiry. The inquiry is designed to arrive at a meeting of the minds and result in mutual commitments between the salesperson and the prospect by determining whether: A. The prospect needs, wants, and can afford our product; B. The prospect is willing to define his Conditions of Satisfaction which, if met, will result in the purchase of our product; and, C. The commitment the prospect makes with regard to his Conditions of Satisfaction is specific as to all the necessary particulars and is absolute and unequivocal.

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#### Annotation 1753202953484

 "On what basis, if any, would you be willing to have us supply some of your packaging materials - as a second source supplier?" The prospect asked what she meant by that, and she said, "Would the right price, or fast delivery, or guaranteed top quality be a deciding factor?"

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#### Annotation 1753204526348

 #vector-space a norm is a function that assigns a strictly positive length or size to each vector (bar zero vector) in a vector space

Norm (mathematics) - Wikipedia
analysis. For field theory, see Field norm. For ideals, see Ideal norm. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional analysis, and related areas of mathematics, <span>a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

#### Flashcard 1753207409932

Tags
#vector-space
Question
a norm is a [...] that assigns a strictly positive length or size to each vector in a vector space
function

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a norm is a function that assigns a strictly positive length or size to each vector in a vector space

#### Original toplevel document

Norm (mathematics) - Wikipedia
analysis. For field theory, see Field norm. For ideals, see Ideal norm. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional analysis, and related areas of mathematics, <span>a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

#### Flashcard 1753209769228

Tags
#vector-space
Question
a norm is a function that assigns a [...] to each vector in a vector space
nonnegative length or size

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#### Parent (intermediate) annotation

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a norm is a function that assigns a strictly positive length or size to each vector (bar zero vector) in a vector space

#### Original toplevel document

Norm (mathematics) - Wikipedia
analysis. For field theory, see Field norm. For ideals, see Ideal norm. For group theory, see Norm (group). For norms in descriptive set theory, see prewellordering. In linear algebra, functional analysis, and related areas of mathematics, <span>a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero. A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

#### Annotation 1753267178764

 #incremental-reading The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading.

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Annotation 1753270062348

 #incremental-reading The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention.

#### Parent (intermediate) annotation

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The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditio

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Annotation 1753271635212

 #incremental-reading With incremental reading, you ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable to traditional book reading.

#### Parent (intermediate) annotation

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The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading.

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Flashcard 1753273208076

Tags
Question
incremental reading helps balance [...] and [...]
speed and retention

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#### Parent (intermediate) annotation

Open it
The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention.

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Flashcard 1753276353804

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Question
With incremental reading, you ensure high-retention of [...]
the most important pieces of text

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With incremental reading, you ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable to typical of traditional book reading.

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Flashcard 1753278713100

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Question
With incremental reading, the majority of time should still be spent on reading at [...].
normal speed

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With incremental reading, you ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable to traditional book reading.

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Flashcard 1753280285964

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Question
With incremental reading, [...how much...] time will be spent reading at speeds comparable to traditional book reading.
a large proportion

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With incremental reading, you ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable to traditional book reading.

#### Original toplevel document

ng and 10% of your time on adding most important findings to SuperMemo, your reading speed will actually decline only by some 10%, while the retention of the most important pieces will be as high as programmed in SuperMemo (up to 99%). <span>The concept of incremental reading introduced in SuperMemo 2000 provides you with a precise tool for finding the optimum balance between speed and retention. You will ensure high-retention of the most important pieces of text, while a large proportion of time will be spent reading at speeds comparable or higher than those typical of traditional book reading. It is worth noting that the learning speed limit in high-retention learning is imposed by your memory. If one-book-per-year sounds like a major disappointment, the roots of this lay

#### Annotation 1753281858828

 #calculus Euler's formula establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

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Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imagina

#### Original toplevel document

Euler's formula - Wikipedia
s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

#### Annotation 1753283431692

 #calculus Euler's formula states that with the argument x given in radians.

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span> Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. <span><body><html>

#### Original toplevel document

Euler's formula - Wikipedia
s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

#### Flashcard 1753285790988

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#calculus
Question
Euler's formula establishes the fundamental relationship between the trigonometric functions and [...]

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#### Parent (intermediate) annotation

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Euler's formula establishes the fundamental relationship between the trigonometric functions and the complex exponential function.

#### Original toplevel document

Euler's formula - Wikipedia
s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

#### Flashcard 1753288150284

Tags
#calculus
Question

Euler's formula states that [...], with the argument x given in radians

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Euler's formula states that with the argument x given in radians.

#### Original toplevel document

Euler's formula - Wikipedia
s formula half-lives exponential growth and decay Defining e proof that e is irrational representations of e Lindemann–Weierstrass theorem People John Napier Leonhard Euler Related topics Schanuel's conjecture v t e <span>Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number x e i x = cos ⁡ x + i sin ⁡ x , {\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more

#### Annotation 1753293131020

 #fourier-analysis the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis.

Fourier analysis - Wikipedia
, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, <span>the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize t

#### Annotation 1753294703884

 #fourier-analysis the original concept of Fourier analysis has been extended to apply to more and more abstract and general situations, and is often known as harmonic analysis.

Fourier analysis - Wikipedia
ions. The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, <span>the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis (see list of Fourier-related transforms) has a corresponding inverse transform that can be used for synthesis. Contents [hide] 1 Application

#### Flashcard 1753296276748

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#fourier-analysis
Question
The reverse of Fourier analysis is known as [...].
Fourier synthesis

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the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis.

#### Original toplevel document

Fourier analysis - Wikipedia
, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, <span>the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis. For example, determining what component frequencies are present in a musical note would involve computing the Fourier transform of a sampled musical note. One could then re-synthesize t

#### Flashcard 1753298636044

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#fourier-analysis
Question
Fourier analysis has been extended to [...].
harmonic analysis

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the original concept of Fourier analysis has been extended to apply to more and more abstract and general situations, and is often known as harmonic analysis.

#### Original toplevel document

Fourier analysis - Wikipedia
ions. The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed. Moreover, <span>the original concept of Fourier analysis has been extended over time to apply to more and more abstract and general situations, and the general field is often known as harmonic analysis. Each transform used for analysis (see list of Fourier-related transforms) has a corresponding inverse transform that can be used for synthesis. Contents [hide] 1 Application

#### Annotation 1753300208908

 #metric #metric-space #topological-space In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.

Metric space - Wikipedia
her, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space. <span>In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them. Other metric spaces occur for example in elliptic geometry and h

#### Annotation 1753303092492

 [unknown IMAGE 1753305451788] #has-images Euclid's parallel postulate: If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.

Parallel postulate - Wikipedia
Parallel postulate - Wikipedia Parallel postulate From Wikipedia, the free encyclopedia Jump to: navigation, search [imagelink] If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It

#### Flashcard 1753308335372

Tags
#has-images
[unknown IMAGE 1753305451788]
Question
Euclid's parallel postulate:
If [...], the two straight lines, produced indefinitely, meet on that side.
the sum of the interior angles α and β is less than 180°

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Euclid's parallel postulate: If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side.

#### Original toplevel document

Parallel postulate - Wikipedia
Parallel postulate - Wikipedia Parallel postulate From Wikipedia, the free encyclopedia Jump to: navigation, search [imagelink] If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It

#### Flashcard 1753310694668

Tags
#metric-space #topological-space
Question
"metric" is a generalization of [...]
the Euclidean distance

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In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.

#### Original toplevel document

Metric space - Wikipedia
her, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space. <span>In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them. Other metric spaces occur for example in elliptic geometry and h

#### Annotation 1753314888972

 #elliptic-geometry Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

Elliptic geometry - Wikipedia
Jyeṣṭhadeva Descartes Pascal Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Present day Atiyah Gromov [imagelink] Geometry portal v t e <span>Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold. Elliptic geometry is studied in two, three, or more dimensions. The appearance of this geometry in the nineteenth century stimulated the development of non-Euclidean geometry generally,

#### Flashcard 1753316461836

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#elliptic-geometry
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Elliptic geometry is a geometry in which [...] does not hold.

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Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

#### Original toplevel document

Elliptic geometry - Wikipedia
Jyeṣṭhadeva Descartes Pascal Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Present day Atiyah Gromov [imagelink] Geometry portal v t e <span>Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold. Elliptic geometry is studied in two, three, or more dimensions. The appearance of this geometry in the nineteenth century stimulated the development of non-Euclidean geometry generally,

#### Flashcard 1753318034700

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#elliptic-geometry
Question
[...] is a geometry in which Euclid's parallel postulate does not hold.
Elliptic geometry

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Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold.

#### Original toplevel document

Elliptic geometry - Wikipedia
Jyeṣṭhadeva Descartes Pascal Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Present day Atiyah Gromov [imagelink] Geometry portal v t e <span>Elliptic geometry is a geometry in which Euclid's parallel postulate does not hold. Elliptic geometry is studied in two, three, or more dimensions. The appearance of this geometry in the nineteenth century stimulated the development of non-Euclidean geometry generally,

#### Annotation 1753319607564

 #metric-space #topological-space A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces.

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In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces.

#### Original toplevel document

Metric space - Wikipedia
Metric space - Wikipedia Metric space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space. In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known propertie

#### Flashcard 1753321180428

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#metric-space #topological-space
Question
A metric on a space induces [...] like open and closed sets
topological properties

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A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces.

#### Original toplevel document

Metric space - Wikipedia
Metric space - Wikipedia Metric space From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, a metric space is a set for which distances between all members of the set are defined. Those distances, taken together, are called a metric on the set. A metric on a space induces topological properties like open and closed sets, which lead to the study of more abstract topological spaces. The most familiar metric space is 3-dimensional Euclidean space. In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known propertie

#### Annotation 1753323539724

 #topology The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.

Open set - Wikipedia
set can be open (called the discrete topology), or no set can be open but the space itself and the empty set (the indiscrete topology). In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. <span>The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets. Each choice of o

#### Flashcard 1753325899020

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#topology
Question
The notion of an [...] provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.
open set

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The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.

#### Original toplevel document

Open set - Wikipedia
set can be open (called the discrete topology), or no set can be open but the space itself and the empty set (the indiscrete topology). In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. <span>The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets. Each choice of o

#### Flashcard 1753327471884

Tags
#topology
Question
The notion of an open set provides a fundamental way to speak of [...] in a topological space, without explicitly having a concept of distance defined.
nearness of points

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The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.

#### Original toplevel document

Open set - Wikipedia
set can be open (called the discrete topology), or no set can be open but the space itself and the empty set (the indiscrete topology). In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. <span>The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets. Each choice of o

#### Flashcard 1753329044748

Tags
#topology
Question
The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of [...] defined.
distance

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The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined.

#### Original toplevel document

Open set - Wikipedia
set can be open (called the discrete topology), or no set can be open but the space itself and the empty set (the indiscrete topology). In practice, however, open sets are usually chosen to be similar to the open intervals of the real line. <span>The notion of an open set provides a fundamental way to speak of nearness of points in a topological space, without explicitly having a concept of distance defined. Once a choice of open sets is made, the properties of continuity, connectedness, and compactness, which use notions of nearness, can be defined using these open sets. Each choice of o

#### Annotation 1753330617612

 #topological-properties In topology, a homeomorphism is a continuous function between topological spaces that has a continuous inverse function.

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In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a

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Homeomorphism - Wikipedia
formation between a coffee mug and a donut (torus) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse function. <span>In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ὅμοιος (homoios) = similar or same (French pareil) and μορφή (morphē) = shape, form, introduced to mathematics by Henri Poincaré in 189

#### Flashcard 1753332976908

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#topological-properties
Question
In topology, a [...] is a continuous function between topological spaces that has a continuous inverse function.
homeomorphism

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In topology, a homeomorphism is a continuous function between topological spaces that has a continuous inverse function.

#### Original toplevel document

Homeomorphism - Wikipedia
formation between a coffee mug and a donut (torus) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse function. <span>In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are the isomorphisms in the category of topological spaces—that is, they are the mappings that preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. The word homeomorphism comes from the Greek words ὅμοιος (homoios) = similar or same (French pareil) and μορφή (morphē) = shape, form, introduced to mathematics by Henri Poincaré in 189

#### Annotation 1753334549772

 #topology The definition of a topological space relies only upon set theory

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The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence.

#### Original toplevel document

Topological space - Wikipedia
, search In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. <span>The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence. [1] Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a centra

#### Flashcard 1753336122636

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#topology
Question
The definition of a topological space relies only upon [...]
set theory

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The definition of a topological space relies only upon set theory

#### Original toplevel document

Topological space - Wikipedia
, search In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighbourhoods for each point, satisfying a set of axioms relating points and neighbourhoods. <span>The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence. [1] Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints. Being so general, topological spaces are a centra

#### Annotation 1753342414092

 #investopedia A proxy statement is a document containing the information the SEC requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting.

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A proxy statement is a document containing the information the Securities and Exchange Commission (SEC) requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting. Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for di

#### Original toplevel document

Proxy Statement
[imagelink] <span>What is a 'Proxy Statement' A proxy statement is a document containing the information the Securities and Exchange Commission (SEC) requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting. Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for directors, and any declarations made by the company's management. BREAKING DOWN 'Proxy Statement' A proxy statement must be filed by a publicly traded company before shareholder meetings, and it discloses material

#### Annotation 1753344773388

 #investopedia Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for directors, and any declarations made by the company's management.

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ntaining the information the Securities and Exchange Commission (SEC) requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting. <span>Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for directors, and any declarations made by the company's management. <span><body><html>

#### Original toplevel document

Proxy Statement
[imagelink] <span>What is a 'Proxy Statement' A proxy statement is a document containing the information the Securities and Exchange Commission (SEC) requires companies to provide to shareholders so shareholders can make informed decisions about matters that will be brought up at an annual or special stockholder meeting. Issues covered in a proxy statement can include proposals for new additions to the board of directors, information on directors' salaries, information on bonus and options plans for directors, and any declarations made by the company's management. BREAKING DOWN 'Proxy Statement' A proxy statement must be filed by a publicly traded company before shareholder meetings, and it discloses material

#### Flashcard 1753346870540

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Question

Who is responsible for the form and content pf the financial statements?

Management

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#### Annotation 1753361288460

 #bascula-session #has-images #reading-embudo Under IFRS, the income statement may be presented as a separate statement followed by a statement of comprehensive income that begins with the profit or loss from the income statement or as a section of a single statement of comprehensive income.

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Under IFRS , the income statement may be presented as a separate statement followed by a statement of comprehensive income that begins with the profit or loss from the income statement or as a section of a single statement of comprehensive income. US GAAP permit the same alternative presentation formats.2 This reading focuses on the income statement, but also discusses comprehensive income (profit or loss from the income statem

#### Original toplevel document

Reading 24  Understanding Income Statements Intro
The income statement presents information on the financial results of a company’s business activities over a period of time. The income statement communicates how much revenue the company generated during a period and what costs it incurred in connection with generating that revenue. The basic equation underlying the income statement, ignoring gains and losses, is Revenue minus Expenses equals Net income. The income statement is also sometimes referred to as the “statement of operations,” “statement of earnings,” or “profit and loss (P&L) statement.” Under International Financial Reporting Standards (IFRS), the income statement may be presented as a separate statement followed by a statement of comprehensive income that begins with the profit or loss from the income statement or as a section of a single statement of comprehensive income.1 US generally accepted accounting principles (US GAAP) permit the same alternative presentation formats.2 This reading focuses on the income statement, but also discusses comprehensive income (profit or loss from the income statement plus other comprehensive income). Investment analysts intensely scrutinize companies’ income statements.3 Equity analysts are interested in them because equity markets often reward relatively high- or low-earnings growth companies with above-average or below-average valuations, respectively, and because inputs into valuation models often include estimates of earnings. Fixed-income analysts examine the components of income statements, past and projected, for information on companies’ abilities to make promised payments on their debt over the course of the business cycle. Corporate financial announcements frequently emphasize information reported in income statements, particularly earnings, more than information reported in the other financial statements. This reading is organized as follows: Section 2 describes the components of the income statement and its format. Section 3 describes basic principles and selected applicati

#### Annotation 1753362861324

 #bascula-session #has-images #reading-embudo US GAAP permit the same alternative presentation formats.2 This reading focuses on the income statement, but also discusses comprehensive income (profit or loss from the income statement plus other comprehensive income).

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IFRS , the income statement may be presented as a separate statement followed by a statement of comprehensive income that begins with the profit or loss from the income statement or as a section of a single statement of comprehensive income. <span>US GAAP permit the same alternative presentation formats.2 This reading focuses on the income statement, but also discusses comprehensive income (profit or loss from the income statement plus other comprehensive income). <span><body><html>

#### Original toplevel document

Reading 24  Understanding Income Statements Intro
The income statement presents information on the financial results of a company’s business activities over a period of time. The income statement communicates how much revenue the company generated during a period and what costs it incurred in connection with generating that revenue. The basic equation underlying the income statement, ignoring gains and losses, is Revenue minus Expenses equals Net income. The income statement is also sometimes referred to as the “statement of operations,” “statement of earnings,” or “profit and loss (P&L) statement.” Under International Financial Reporting Standards (IFRS), the income statement may be presented as a separate statement followed by a statement of comprehensive income that begins with the profit or loss from the income statement or as a section of a single statement of comprehensive income.1 US generally accepted accounting principles (US GAAP) permit the same alternative presentation formats.2 This reading focuses on the income statement, but also discusses comprehensive income (profit or loss from the income statement plus other comprehensive income). Investment analysts intensely scrutinize companies’ income statements.3 Equity analysts are interested in them because equity markets often reward relatively high- or low-earnings growth companies with above-average or below-average valuations, respectively, and because inputs into valuation models often include estimates of earnings. Fixed-income analysts examine the components of income statements, past and projected, for information on companies’ abilities to make promised payments on their debt over the course of the business cycle. Corporate financial announcements frequently emphasize information reported in income statements, particularly earnings, more than information reported in the other financial statements. This reading is organized as follows: Section 2 describes the components of the income statement and its format. Section 3 describes basic principles and selected applicati

#### Annotation 1753378589964

 Don't waste your resources on Low Probability Prospects

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#### Annotation 1753380162828

 Keep in mind that the intangible emotional drain on the salesperson of working with a low probability prospect is a hidden, but very considerable, additional cost.

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#### Annotation 1753382784268

 In a traditional sales situation, the salesperson and the customer are adversaries. It's hard to have a sincere relationship with your enemy. In High Probability Selling the object is to build a relationship based on mutual trust and respect. In order to do that it's necessary to find out who the prospect really is. The salesperson gets ripped off with anything less. If the prospect isn't open and honest with us, we don't deal with him.

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#### Annotation 1753385143564

 High Probability Selling is very different. First, we clarify what it is the prospect wants, and we both agree on exactly what those wants are. We call those wants the prospect's Conditions Of Satisfaction. Second, assuming we can fulfill those Conditions Of Satisfaction profitably, we negotiate mutual commitments. In other words, we get crystal clear on what each of us promises to do. When you're negotiating commitments, you're into what you've always called the "close.

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#### Annotation 1753386716428

 We should be almost always asking instead of telling. You should frame most of what you have to say in the form of a question. The prospect should do most of the talking, primarily answering your questions. The more the prospect talks, the more both of you win.

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#### Annotation 1753389075724

 The more you try to convince the prospect that your product or service is the best, the more resistance you create.

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#### Annotation 1753391435020

 Understand this, almost anything you say can be phrased as a question. As long as you're asking questions, the prospect remains involved in the conversation.

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#### Annotation 1753393270028

 Do you prefer to have...?

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#### Annotation 1753395629324

 Yes, is that what you want?

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#### Annotation 1753397464332

 Are you willing to pay more for top quality and on-time delivery of service?

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#### Annotation 1753401920780

 When you're focusing on what the prospect has to say, your ideas on how to serve him are welcomed, especially when those ideas are phrased as questions.

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#### Annotation 1753404280076

 What else do you want?

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 Gathering information isn't closing.

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#### Annotation 1753409522956

 The entire High Probability Selling process is a closing process.

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#### Annotation 1754484837644

 The web is the ultimate merit-based marketplace: If you have what they want, they’ll buy it.

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#### Annotation 1754486410508

 you can literally be up and running with a full-featured web site for well under \$100.

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 create a product for next to no money and for just a little bit of your time

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#### Annotation 1754489556236

 You don’t need big blocks of time to get a six-figure second income. All you need is scraps of time here and there.

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#### Annotation 1754491129100

 people can get things done on their own without being told what to do and when to do it. Are you one of these people?

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#### Annotation 1754492701964

 The real trick is to know your very next step to take and to take small actions regularly.

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#### Annotation 1754494274828

 some people out there are ready-and- willing buyers right now. It’s a matter of finding them

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#### Annotation 1754495847692

 we’re living in a society where the pace of new good ideas is getting quicker

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#### Annotation 1754497420556

 Most people are collectors of things. They don’t buy just one book but lots of them. They don’t have one cat but several. They don’t stop with one screwdriver, casserole recipe, or dog leash, but they own many.

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#### Annotation 1754499779852

 Everywhere you look, the old model of big, slow, and one-size-fits-all, is giving way to fast, agile, and just-the-way-you-want-it. This is wonderful news for the micromanufacturer and micromarketer you’ll become

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#### Annotation 1754501614860

 Can you turn on your computer and use a mouse? Can you read plain text on the screen? Okay then, you’re good to go.