# on 13-Feb-2018 (Tue)

#### Flashcard 1729653247244

Tags
#topology
Question
In geometry, an affine transformation preserves [...objects...].
points, straight lines and planes

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In geometry, an affine transformation, affine map [1] or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes.

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Affine transformation - Wikipedia
s related to each other leaf by an affine transformation. For instance, the red leaf can be transformed into both the small dark blue leaf and the large light blue leaf by a combination of reflection, rotation, scaling, and translation. <span>In geometry, an affine transformation, affine map [1] or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. Examples of affine transformations include translation, scaling, homothety, similarity transformation, reflection, rotation, shear mapping, and compositions of them in any combination

#### Flashcard 1729692830988

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#multivariate-normal-distribution
Question

In the bivariate normal case the expression for the mutual information is [...]

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In the bivariate case the expression for the mutual information is:

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Multivariate normal distribution - Wikipedia
ldsymbol {\rho }}_{0}} is the correlation matrix constructed from Σ 0 {\displaystyle {\boldsymbol {\Sigma }}_{0}} . <span>In the bivariate case the expression for the mutual information is: I ( x ; y ) = − 1 2 ln ⁡ ( 1 − ρ 2 ) . {\displaystyle I(x;y)=-{1 \over 2}\ln(1-\rho ^{2}).} Cumulative distribution function[edit source] The notion of cumulative distribution function (cdf) in dimension 1 can be extended in two ways to the multidimensional case, based

#### Flashcard 1730170981644

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#matrix-decomposition
Question
Computers usually solve square systems of linear equations using [...]
the LU decomposition

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Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix.

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LU decomposition - Wikipedia
rization) factors a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. The LU decomposition can be viewed as the matrix form of Gaussian elimination. <span>Computers usually solve square systems of linear equations using the LU decomposition, and it is also a key step when inverting a matrix, or computing the determinant of a matrix. The LU decomposition was introduced by mathematician Tadeusz Banachiewicz in 1938. [1] Contents [hide] 1 Definitions 1.1 LU factorization with Partial Pivoting 1.2 LU facto

#### Flashcard 1731684601100

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#dynamic-programming
Question
subproblem solutions are typically indexed by [...] to facilitate lookup.
input values

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tion, 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 <span>the values of its input parameters, so as to facilitate its lookup.) <span><body><html>

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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 1731738340620

Tags
#stochastics
Question

in the Wiener process , is normally distributed with [...

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r process is characterised by the following properties: [1] a.s. has independent increments: for every the future increments , are independent of the past values , has Gaussian increments: is normally distributed with <span>mean and variance , has continuous paths: With probability , is continuous in . <span><body><html>

#### Original toplevel document

Wiener process - Wikipedia
Brownian motion 4.3 Time change 4.4 Change of measure 4.5 Complex-valued Wiener process 4.5.1 Self-similarity 4.5.2 Time change 5 See also 6 Notes 7 References 8 External links Characterisations of the Wiener process[edit source] <span>The Wiener process W t {\displaystyle W_{t}} is characterised by the following properties: [1] W 0 = 0 {\displaystyle W_{0}=0} a.s. W {\displaystyle W} has independent increments: for every t > 0 , {\displaystyle t>0,} the future increments W t + u − W t , {\displaystyle W_{t+u}-W_{t},} u ≥ 0 , {\displaystyle u\geq 0,} , are independent of the past values W s {\displaystyle W_{s}} , s ≤ t . {\displaystyle s\leq t.} W {\displaystyle W} has Gaussian increments: W t + u − W t {\displaystyle W_{t+u}-W_{t}} is normally distributed with mean 0 {\displaystyle 0} and variance u {\displaystyle u} , W t + u − W t ∼ N ( 0 , u ) . {\displaystyle W_{t+u}-W_{t}\sim {\mathcal {N}}(0,u).} W {\displaystyle W} has continuous paths: With probability 1 {\displaystyle 1} , W t {\displaystyle W_{t}} is continuous in t {\displaystyle t} . The independent increments means that if 0 ≤ s 1 < t 1 ≤ s 2 < t 2 then W t 1 −W s 1 and W t 2 −W s 2 are independent random variables, and the similar condition holds for

#### Flashcard 1732343631116

Tags
#logic
Question
J M Bocheński wrote [...] in 1961
A History of Formal Logic

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According to A History of Formal Logic (1961) by the distinguished J M Bocheński, the golden periods for logic were the ancient Greek period, the medieval scholastic period, and the mathematical period of the 19th and 20th centurie

#### Original toplevel document

The rise and fall and rise of logic | Aeon Essays
the hands of thinkers such as George Boole, Gottlob Frege, Bertrand Russell, Alfred Tarski and Kurt Gödel, it’s clear that Kant was dead wrong. But he was also wrong in thinking that there had been no progress since Aristotle up to his time. <span>According to A History of Formal Logic (1961) by the distinguished J M Bocheński, the golden periods for logic were the ancient Greek period, the medieval scholastic period, and the mathematical period of the 19th and 20th centuries. (Throughout this piece, the focus is on the logical traditions that emerged against the background of ancient Greek logic. So Indian and Chinese logic are not included, but medieval Ara

#### Flashcard 1732737633548

Tags
#linear-algebra
Question

a bilinear form is [...descriptive]

linear in each argument separately

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In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K , where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is <span>linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) <span><body><html>

#### Original toplevel document

Bilinear form - Wikipedia
Bilinear form - Wikipedia Bilinear form From Wikipedia, the free encyclopedia Jump to: navigation, search In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map V × V → K, where K is the field of scalars. In other words, a bilinear form is a function B : V × V → K that is linear in each argument separately: B(u + v, w) = B(u, w) + B(v, w) and B(λu, v) = λB(u, v) B(u, v + w) = B(u, v) + B(u, w) and B(u, λv) = λB(u, v) The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms. When K is the field of complex numbers C, one

#### Flashcard 1737321745676

Question
the Black–Scholes equation governs [...] of a European call or European put
the price evolution

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In mathematical finance, the Black–Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black–Scholes model.

#### Original toplevel document

Black–Scholes equation - Wikipedia

#### Flashcard 1737355824396

Question
update conda with [...] if you haven't update it for a long time.
conda update conda

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Before you proceed to conda update --all command to update all packages in an environment, first update conda with conda update conda command if you haven't update it for a long time.

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python - Bulk package updates using Conda [Anaconda] - Stack Overflow
add a comment | up vote 4 down vote <span>Before you proceed to conda update --all command, first update conda with conda update conda command if you haven't update it for a long time. It happent to me (Python 2.7.13 on Anaconda 64 bits). share|edit|flag edited Dec 26 '17 at 4:42 [imagelink]

#### Flashcard 1739082566924

Tags
#forward-backward-algorithm #hmm
Question
The foreward-backward algorithm obtain [...] in two passes.
the posterior marginal distributions

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The foreward-backward algorithm makes use of the principle of dynamic programming to compute efficiently the values that are required to obtain the posterior marginal distributions in two passes. The first pass goes forward in time while the second goes backward in time; hence the name forward–backward algorithm.

#### Original toplevel document

Forward–backward algorithm - Wikipedia
| o 1 : t ) {\displaystyle P(X_{k}\ |\ o_{1:t})} . This inference task is usually called smoothing. <span>The algorithm makes use of the principle of dynamic programming to compute efficiently the values that are required to obtain the posterior marginal distributions in two passes. The first pass goes forward in time while the second goes backward in time; hence the name forward–backward algorithm. The term forward–backward algorithm is also used to refer to any algorithm belonging to the general class of algorithms that operate on sequence models in a forward–backward manner. I

#### Flashcard 1739212852492

Tags
#d-separation
Question
the "d" in terms "d-separated" and "d-connected" accounts for [...]
the orientations of the arrows

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dea is to define what we mean by "connecting path", given that we are dealing with a system of directed arrows in the graph some vertices correspond to measured variables, whose values are known precisely. To account for <span>the orientations of the arrows we use the terms "d-separated" and "d-connected" (d connotes "directional"). <span><body><html>

#### Original toplevel document

Unknown title
d-SEPARATION WITHOUT TEARS (At the request of many readers) Introduction d-separation is a criterion for deciding, from a given a causal graph, whether a set X of variables is independent of another set Y, given a third set Z. <span>The idea is to associate "dependence" with "connectedness" (i.e., the existence of a connecting path) and "independence" with "unconnected-ness" or "separation". The only twist on this simple idea is to define what we mean by "connecting path", given that we are dealing with a system of directed arrows in which some vertices (those residing in Z) correspond to measured variables, whose values are known precisely. To account for the orientations of the arrows we use the terms "d-separated" and "d-connected" (d connotes "directional"). We start by considering separation between two singleton variables, x and y; the extension to sets of variables is straightforward (i.e., two sets are separated if and only if each el

#### Flashcard 1741091114252

Tags
#measure-theory
Question
Technically, a measure is a function that assigns [...] to (certain) subsets of a set X
a non-negative real number or +∞

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Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (see Definition below). It must further be countably additive:

#### Original toplevel document

Measure (mathematics) - Wikipedia
[imagelink] Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. <span>In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the Lebesgue measure on a Euclidean space, which assigns the conventional length, area, and volume of Euclidean geometry to suitable subsets of the n-dimensional Euclidean space R n . For instance, the Lebesgue measure of the interval [0, 1] in the real numbers is its length in the everyday sense of the word – specifically, 1. Technically, a measure is a function that assigns a non-negative real number or +∞ to (certain) subsets of a set X (see Definition below). It must further be countably additive: the measure of a 'large' subset that can be decomposed into a finite (or countably infinite) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a consistent size to each subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the counting measure. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called measurable subsets, which are required to form a σ-algebra. This means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. [1] Indeed, their existence is a non-trivial consequence of the axiom of choice. Measure theory was developed in successive stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon, and Maurice Fréchet, among others. The ma

#### Annotation 1744016379148

 #metric-space #topological-space 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.

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 1744282979596

Tags
#metric-space #topological-space
Question
In mathematics, a metric space is a set for which [...].
distances between all members of the set are defined

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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

#### 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 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

#### 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 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

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

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#### Parent (intermediate) annotation

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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 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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 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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 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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#### Annotation 1753407163660

 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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#### Annotation 1754487983372

 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.

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 #metric-space #topological-space Other metric spaces occur for example in elliptic geometry and hyperbolic geometry, where distance on a sphere measured by angle is a metric

Metric space - Wikipedia
uot; 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. <span>Other metric spaces occur for example in elliptic geometry and hyperbolic geometry, where distance on a sphere measured by angle is a metric, and the hyperboloid model of hyperbolic geometry is used by special relativity as a metric space of velocities. Contents 1 History 2 Definition 3 Examples of metric spaces 4

#### Annotation 1754519964940

 You do need to be clear and direct in what you offer people, and that’s easy to accomplish

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#### Annotation 1754522586380

 It’s much less painful and much more profitable to have your business in an area that’s already somewhat established.

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 Most of your competition is not very good at selling

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#### Annotation 1754526780684

 Most businesses do a bland-to-terrible job of customer service. They make the really good companies stand out, and that’s the kind of business you should create. Really savvy marketers have a rule: For fastest revenue growth, look for businesses with an existing, installed base of customers. It’s smart advice.

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 On the web, nobody cares about your background. In the Internet world, clients could not care less.

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#### Annotation 1754537528588

 You can’t let your overactive protection instinct squash your business idea altogether. If you let that happen then it might as well be a thief breaking into your house and stealing all your business ideas—either way, you’re left with nothing to show for your asset. It’s much better to launch your product—even if it’s not perfect—and start to make money with it.

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#### Annotation 1754546441484

 people who believe some of these 10 mistaken notions. You might even be one of them. Do you see how powerful it will be when this book shows you how to navigate past these false barriers but your competition is stuck with them? That’s why I say you should thank your lucky stars for all the half-truths, myths, and bad information surrounding online businesses.

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 you really should concern yourself with—the true barriers to your progress.

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 We all have people around us who mean well with their advice, but in reality they’re not that helpful and not that successful themselves. It’s very dangerous for you to take advice from them.

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#### Annotation 1754554043660

 That’s absurd. I don’t think I can sit on the couch and make money!

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#### Annotation 1754555878668

 There’s no question that many people work extremely hard for their money. The mental limitation comes when they think that only through hard work can they produce honest money. It seems that some people apply moral overtones and believe that easy money is only what thieves can get away with.

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#### Annotation 1754558237964

 making an information product one time and selling it for years or even decades afterward. Oh, you should update the information from time to time, but fundamentally you have done the work once and now will receive an income stream for a very long time.

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 don’t have some moral or religious aversion to making money without shedding any blood, sweat, or tears.

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 It’s simply not necessary to take great risks or step way outside of your comfort zone in order to make a lot of money, but stretching that zone is a good thing

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 a stretched and limber brain will make you more money.

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#### Annotation 1754567413004

 ’ve made many millions of dollars in real estate and have never found it necessary to knock on door after door. Instead I use direct mail. I created a series of letters and figured out where to get good-quality lists of motivated sellers of real estate.

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 most people have highly developed excuse generators

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#### Annotation 1754574490892

 look for ways you might adapt something to work. Look at each interesting idea or success you hear about as a potential foothold. It might only be something you can jamb your foot into with some effort, but you will now be a step higher than you were before

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#### Annotation 1754576325900

 begin to recognize that decidedly unhelpful voice in your brain and stick it off in a corner

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 the good news is that plenty of methods still work just fine for making money online. No single method is revolutionary, just as nothing is the single super-food you probably want to eat for the rest of your life to the exclusion of all else.

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 with steady effort it begins to work

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 By all means keep your eyes open for the next technology that can make your life easier

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#### Annotation 1754582879500

 simply look for how it might fit into what you already have in place

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 All these barriers and dangers are great for you because they mean less competition.

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 I suggest you review those sections regularly. It’s so easy to be lulled back into thinking in those old, counterproductive ways

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 see opportunity and potential profits just about everywhere you look.

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#### Annotation 1754590481676

 Free morphemes can function independently as words (e.g. town, dog) and can appear within lexemes (e.g. town hall, doghouse).Bound morphemes appear only as parts of words, always in conjunction with a root and sometimes with other bound morphemes. For example, un- appears only accompanied by other morphemes to form a word. Most bound morphemes in English are affixes, particularly prefixes and suffixes. Examples of suffixes are -tion, -ation, -ible, -ing, etc. Bound morphemes that are not affixes are called cranberry morphemes.

Morpheme - Wikipedia
nd bound morphemes Main article: Bound and unbound morphemes Every morpheme can be classified as either free or bound. [2] These categories are mutually exclusive, and as such, a given morpheme will belong to exactly one of them. <span>Free morphemes can function independently as words (e.g. town, dog) and can appear within lexemes (e.g. town hall, doghouse). Bound morphemes appear only as parts of words, always in conjunction with a root and sometimes with other bound morphemes. For example, un- appears only accompanied by other morphemes to form a word. Most bound morphemes in English are affixes, particularly prefixes and suffixes. Examples of suffixes are -tion, -ation, -ible, -ing, etc. Bound morphemes that are not affixes are called cranberry morphemes. Classification of bound morphemes Bound morphemes can be further classified as derivational or inflectional. Derivational morphemes Derivational morphemes, when comb

#### Annotation 1754595462412

 #topological-properties homeomorphic spaces are topologically the same.

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unction 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. <span>Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same. <span><body><html>

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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 1754597821708

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#topological-properties
Question
[...] spaces are topologically the same.
homeomorphic

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homeomorphic spaces are topologically the same.

#### 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

#### Flashcard 1754599394572

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#topology
Question
[...] is the most general notion of a mathematical space
topological space

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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.

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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 1754601753868

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topological space allows for the definition of concepts such as [...CCC...] .

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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

#### Annotation 1754604113164

 #topology Each choice of open sets for a space is called a topology.

Open set - Wikipedia
pological 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. <span>Each choice of open sets for a space is called a topology. Although open sets and the topologies that they comprise are of central importance in point-set topology, they are also used as an organizational tool in other important branches of mat

#### Annotation 1754607258892

 #topology In particular, sets of the form (-ε, ε) give us a lot of information about points close to x = 0. Thus, rather than speaking of a concrete Euclidean metric, one may use sets to describe points close to x.

Open set - Wikipedia
ese points approximate x to a greater degree of accuracy compared to when ε = 1. The previous discussion shows, for the case x = 0, that one may approximate x to higher and higher degrees of accuracy by defining ε to be smaller and smaller. <span>In particular, sets of the form (-ε, ε) give us a lot of information about points close to x = 0. Thus, rather than speaking of a concrete Euclidean metric, one may use sets to describe points close to x. This innovative idea has far-reaching consequences; in particular, by defining different collections of sets containing 0 (distinct from the sets (-ε, ε)), one may find different result

#### Annotation 1754608831756

 #topology In general, one refers to the family of sets containing 0, used to approximate 0, as a neighborhood basis; a member of this neighborhood basis is referred to as an open set.

Open set - Wikipedia
e find that in some sense, every real number is distance 0 away from 0. It may help in this case to think of the measure as being a binary condition, all things in R are equally close to 0, while any item that is not in R is not close to 0. <span>In general, one refers to the family of sets containing 0, used to approximate 0, as a neighborhood basis; a member of this neighborhood basis is referred to as an open set. In fact, one may generalize these notions to an arbitrary set (X); rather than just the real numbers. In this case, given a point (x) of that set, one may define a collection of sets &q

#### Annotation 1754610404620

 #topology When difining nearness between points with open balls, the measure of distance becomes a binary condition

Open set - Wikipedia
ot;measuring distance", all points are close to 0 since there is only one possible degree of accuracy one may achieve in approximating 0: being a member of R. Thus, we find that in some sense, every real number is distance 0 away from 0. <span>It may help in this case to think of the measure as being a binary condition, all things in R are equally close to 0, while any item that is not in R is not close to 0. In general, one refers to the family of sets containing 0, used to approximate 0, as a neig

#### Flashcard 1754613550348

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#topology
Question
When difining nearness between points with open balls, the measure of distance becomes a [...]
binary condition

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When difining nearness between points with open balls, the measure of distance becomes a binary condition

#### Original toplevel document

Open set - Wikipedia
ot;measuring distance", all points are close to 0 since there is only one possible degree of accuracy one may achieve in approximating 0: being a member of R. Thus, we find that in some sense, every real number is distance 0 away from 0. <span>It may help in this case to think of the measure as being a binary condition, all things in R are equally close to 0, while any item that is not in R is not close to 0. In general, one refers to the family of sets containing 0, used to approximate 0, as a neig

#### Flashcard 1754615123212

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#topology
Question
When difining [...] with open balls, the measure of distance becomes a binary condition
nearness between points

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When difining nearness between points with open balls, the measure of distance becomes a binary condition

#### Original toplevel document

Open set - Wikipedia
ot;measuring distance", all points are close to 0 since there is only one possible degree of accuracy one may achieve in approximating 0: being a member of R. Thus, we find that in some sense, every real number is distance 0 away from 0. <span>It may help in this case to think of the measure as being a binary condition, all things in R are equally close to 0, while any item that is not in R is not close to 0. In general, one refers to the family of sets containing 0, used to approximate 0, as a neig

#### Annotation 1754616696076

 #topology Sets that can be constructed as the intersection of countably many open sets are denoted Gδ sets.

Open set - Wikipedia
u } the open sets. Note that infinite intersections of open sets need not be open. For example, the intersection of all intervals of the form (−1/n, 1/n), where n is a positive integer, is the set {0} which is not open in the real line. <span>Sets that can be constructed as the intersection of countably many open sets are denoted G δ sets. The topological definition of open sets generalizes the metric space definition: If one begins with a metric space and defines open sets as before, then the family of all open sets is

#### Annotation 1754618268940

 #topology infinite intersections of open sets need not be open.

Open set - Wikipedia
τ {\displaystyle \tau } is in τ {\displaystyle \tau } ) We call the sets in τ {\displaystyle \tau } the open sets. Note that <span>infinite intersections of open sets need not be open. For example, the intersection of all intervals of the form (−1/n, 1/n), where n is a positive integer, is the set {0} which is not open in the real line. Sets that can be constructed as

#### Flashcard 1754619841804

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#topology
Question
[...] of open sets need not be open.
infinite intersections

The axiom of sigma-algebra uses infinite (countable) intersections.

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infinite intersections of open sets need not be open.

#### Original toplevel document

Open set - Wikipedia
τ {\displaystyle \tau } is in τ {\displaystyle \tau } ) We call the sets in τ {\displaystyle \tau } the open sets. Note that <span>infinite intersections of open sets need not be open. For example, the intersection of all intervals of the form (−1/n, 1/n), where n is a positive integer, is the set {0} which is not open in the real line. Sets that can be constructed as

#### Annotation 1754623511820

 #topology topology is closed under finite intersections while sigma-algebra is closed under countable intersections

measure theory - Difference between topology and sigma-algebra axioms. - Mathematics Stack Exchange
up vote 11 down vote favorite 6 One distinct difference between axioms of topology and sigma algebra is the asymmetry between union and intersection; meaning <span>topology is closed under finite intersections sigma-algebra closed under countable union. It is very clear mathematically but is there a way to think; so that we can define a geometric difference? In other words I want to have an intuitive idea in application of this object

#### Flashcard 1754626395404

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#topology
Question
topology is closed under [...] intersections while sigma-algebra is closed under [...] intersections
finite, countable

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topology is closed under finite intersections while sigma-algebra is closed under countable intersections

#### Original toplevel document

measure theory - Difference between topology and sigma-algebra axioms. - Mathematics Stack Exchange
up vote 11 down vote favorite 6 One distinct difference between axioms of topology and sigma algebra is the asymmetry between union and intersection; meaning <span>topology is closed under finite intersections sigma-algebra closed under countable union. It is very clear mathematically but is there a way to think; so that we can define a geometric difference? In other words I want to have an intuitive idea in application of this object

#### Flashcard 1754629278988

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#topology
Question
Each choice of open sets for a space is called a [...].
topology

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Each choice of open sets for a space is called a topology.

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Open set - Wikipedia
pological 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. <span>Each choice of open sets for a space is called a topology. Although open sets and the topologies that they comprise are of central importance in point-set topology, they are also used as an organizational tool in other important branches of mat

#### Flashcard 1754630851852

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#topology
Question
Each [...] for a space is called a topology.
choice of open sets

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Each choice of open sets for a space is called a topology.

#### Original toplevel document

Open set - Wikipedia
pological 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. <span>Each choice of open sets for a space is called a topology. Although open sets and the topologies that they comprise are of central importance in point-set topology, they are also used as an organizational tool in other important branches of mat

#### Annotation 1754632424716

 #topology A complement of an open set (relative to the space that the topology is defined on) is called a closed set.

Open set - Wikipedia
l space. There are, however, topological spaces that are not metric spaces. Properties The union of any number of open sets, or infinitely many open sets, is open. [2] The intersection of a finite number of open sets is open. [2] <span>A complement of an open set (relative to the space that the topology is defined on) is called a closed set. A set may be both open and closed (a clopen set). The empty set and the full space are examples of sets that are both open and closed. [3] Uses Open sets have a fundamental im

#### Flashcard 1755466304780

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#topology
Question
[...] is called a closed set.
A complement of an open set

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A complement of an open set (relative to the space that the topology is defined on) is called a closed set.

#### Original toplevel document

Open set - Wikipedia
l space. There are, however, topological spaces that are not metric spaces. Properties The union of any number of open sets, or infinitely many open sets, is open. [2] The intersection of a finite number of open sets is open. [2] <span>A complement of an open set (relative to the space that the topology is defined on) is called a closed set. A set may be both open and closed (a clopen set). The empty set and the full space are examples of sets that are both open and closed. [3] Uses Open sets have a fundamental im

#### Flashcard 1755467877644

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#topology
Question
A complement of an open set is called a [...].
closed set

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A complement of an open set (relative to the space that the topology is defined on) is called a closed set.

#### Original toplevel document

Open set - Wikipedia
l space. There are, however, topological spaces that are not metric spaces. Properties The union of any number of open sets, or infinitely many open sets, is open. [2] The intersection of a finite number of open sets is open. [2] <span>A complement of an open set (relative to the space that the topology is defined on) is called a closed set. A set may be both open and closed (a clopen set). The empty set and the full space are examples of sets that are both open and closed. [3] Uses Open sets have a fundamental im

#### Annotation 1755469450508

 #topology U is open if every point in U has a neighborhood contained in U.

Open set - Wikipedia
ntained in U. Metric spaces A subset U of a metric space (M, d) is called open if, given any point x in U, there exists a real number ε > 0 such that, given any point y in M with d(x, y) < ε, y also belongs to U. Equivalently, <span>U is open if every point in U has a neighborhood contained in U. This generalizes the Euclidean space example, since Euclidean space with the Euclidean distance is a metric space. Topological spaces In general topological spaces, the open

#### Annotation 1755472334092

 #topology Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set.

Neighbourhood (mathematics) - Wikipedia
{\displaystyle V} . In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. <span>Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set. Contents [hide] 1 Definitions 1.1 Neighbourhood of a point 1.2 Neighbourhood of a set 2 In a metric space 3 Examples 4 Topology from neighbourhoods 5 Uniform neighbourhoo

#### Flashcard 1755474431244

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#topology
Question
Intuitively speaking, a [...] is a set of points containing that point where one can move some amount away from that point without leaving the set.
neighbourhood of a point

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Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set.

#### Original toplevel document

Neighbourhood (mathematics) - Wikipedia
{\displaystyle V} . In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. <span>Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount away from that point without leaving the set. Contents [hide] 1 Definitions 1.1 Neighbourhood of a point 1.2 Neighbourhood of a set 2 In a metric space 3 Examples 4 Topology from neighbourhoods 5 Uniform neighbourhoo

#### Annotation 1755478625548

 #optimization In a convex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum

Mathematical optimization - Wikipedia
l of the function values are greater than or equal to the value at that point. Local maxima are defined similarly. While a local minimum is at least as good as any nearby points, a global minimum is at least as good as every feasible point. <span>In a convex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. A large number of algorithms proposed for solving nonconvex problems—including th

#### Annotation 1755480722700

 #optimization A large number of algorithms proposed for solving nonconvex problems—including the majority of commercially available solvers—are not capable of making a distinction between locally optimal solutions and globally optimal solutions

Mathematical optimization - Wikipedia
onvex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. <span>A large number of algorithms proposed for solving nonconvex problems—including the majority of commercially available solvers—are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat the former as actual solutions to the original problem. Global optimization is the branch of applied mathematics and numerical analysis that is concerned with the develo

#### Annotation 1755482295564

 #optimization Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima

Mathematical optimization - Wikipedia
energy functional. A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution. In mathematics, conventional optimization problems are usually stated in terms of minimization. <span>Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima. A local minimum x* is defined as a point for which there exists some δ > 0 such that for all x where ‖ x −

#### Annotation 1755483868428

 #optimization mathematical optimization selects a best element (with regard to some criterion) from some set of available alternatives.

Mathematical optimization - Wikipedia
+ 4. The global maximum at (x, y, z) = (0, 0, 4) is indicated by a blue dot. [imagelink] Nelder-Mead minimum search of Simionescu's function. Simplex vertices are ordered by their value, with 1 having the lowest (best) value. <span>In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives. [1] In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the

#### Flashcard 1755486227724

Tags
#optimization
Question

mathematical optimization selects a [...] (with regard to some criterion) from some set of available alternatives.

best element

there are many answers to this question, but this answer is more intuitive from the measure oriented perspective.

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mathematical optimization selects a best element (with regard to some criterion) from some set of available alternatives.

#### Original toplevel document

Mathematical optimization - Wikipedia
+ 4. The global maximum at (x, y, z) = (0, 0, 4) is indicated by a blue dot. [imagelink] Nelder-Mead minimum search of Simionescu's function. Simplex vertices are ordered by their value, with 1 having the lowest (best) value. <span>In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives. [1] In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the

#### Flashcard 1755492257036

Tags
#optimization
Question
Generally, unless both [...] are convex there may be several local minima
the objective function and the feasible region

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Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima

#### Original toplevel document

Mathematical optimization - Wikipedia
energy functional. A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution. In mathematics, conventional optimization problems are usually stated in terms of minimization. <span>Generally, unless both the objective function and the feasible region are convex in a minimization problem, there may be several local minima. A local minimum x* is defined as a point for which there exists some δ > 0 such that for all x where ‖ x −

#### Flashcard 1755493829900

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#optimization
Question
In a convex problem, if there is a local minimum that is [...], it is also the global minimum
interior

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In a convex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum

#### Original toplevel document

Mathematical optimization - Wikipedia
l of the function values are greater than or equal to the value at that point. Local maxima are defined similarly. While a local minimum is at least as good as any nearby points, a global minimum is at least as good as every feasible point. <span>In a convex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. A large number of algorithms proposed for solving nonconvex problems—including th

#### Flashcard 1755496189196

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#optimization
Question
most algorithms for solving nonconvex problems can't distinguish between [...]
local and global optima

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A large number of algorithms proposed for solving nonconvex problems—including the majority of commercially available solvers—are not capable of making a distinction between locally optimal solutions and globally optimal solutions

#### Original toplevel document

Mathematical optimization - Wikipedia
onvex problem, if there is a local minimum that is interior (not on the edge of the set of feasible points), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima. <span>A large number of algorithms proposed for solving nonconvex problems—including the majority of commercially available solvers—are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat the former as actual solutions to the original problem. Global optimization is the branch of applied mathematics and numerical analysis that is concerned with the develo

#### Annotation 1755498548492

 Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for moving towards an optimum.

Mathematical optimization - Wikipedia
the pairs of the form (5, 2kπ) and (−5,(2k+1)π), where k ranges over all integers. arg min and arg max are sometimes also written argmin and argmax, and stand for argument of the minimum and argument of the maximum. History[edit source] <span>Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for moving towards an optimum. The term "linear programming" for certain optimization cases was due to George B. Dantzig, although much of the theory had been introduced by Leonid Kantorovich in 1939. (Pr

#### Annotation 1755514801420

 McDonald’s chairman Ray Kroc said: “We can invent faster than they can steal.”

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#### Annotation 1755516374284

 even if you didn’t invent faster than the thieves could knock you off, you could always claim to be the genuine article, the first-ever, and urge customers to accept no substitutes.

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#### Annotation 1755517947148

 You only need to find hundreds or perhaps a few thousand people worldwide for your product to make you a very nice pile of dough

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#### Annotation 1755519520012

 make a bunch of money with a product and then you’ll have plenty of resources to go after fame.

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#### Annotation 1755521092876

 Even the mighty Mississippi River starts as a few trickles and then combines over time to become something impressive.

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#### Annotation 1755522927884

 You can make a bundle of money by carving out your corner of an existing product category.

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#### Annotation 1755524500748

 start small, nimble, and cheap

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#### Annotation 1755526073612

 Your first moneymaker should be an information product.

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#### Annotation 1755527646476

 Relatively short process. Can be as short as days.

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#### Annotation 1755529219340

 What Problem Have You Solved?

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#### Annotation 1755530792204

 People want to know the straightforward, quick, easy way to operate things

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#### Annotation 1755532365068

 Think of a solution that either you have found or someone you know has found. turn that solution into an info product.

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#### Annotation 1755534986508

 Be highly efﬁcient. The competition is simply too great to trust mere theory. Therefore use tested and proven methods whenever possible.

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#### Annotation 1755537345804

 You don’t have to implement everything right away. Just take one investing step at a time. The real key to success is to get moving and take those steps.

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#### Annotation 1755538918668

 Here ’ s how a future billionaire thinks: “ The way to become as wealthy as Donald Trump is to start owning commercial property in my town. ”

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#### Annotation 1755882851596

 Commercial property isn ’ t your destination; it ’ s the way you will reach it.

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#### Annotation 1755884686604

 Just what is commercial real estate? It’s Ofﬁce buildings (all the way from skyscrapers down to a small building with a dental ofﬁce in it) Apartment buildings with ﬁve or more units Stores, whether they’re in big malls or small, local shopping centers Hotels and restaurants Industrial space (factories, warehouses, and so on)

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#### Annotation 1755887832332

 The wealth opportunity with commercial real estate is enormous for the very reason that most people think they could never own it.

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#### Annotation 1755889929484

 Thank your lucky stars that commercial real estate remains shrouded in myth and misinformation for millions of real estate investors. They convince themselves that it ’ s not worth doing commercial real estate because they imagine a series of huge barriers in their way.

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#### Annotation 1755892550924

 Here are just three of the many psychological barriers to entry: “ The bigger the building, the bigger the down payment that I need. ” “ I couldn ’ t possibly own a shopping center; I know nothing about retail sales. ” “ All the good deals must have long since been picked over: I ’ ll see only the lousy ones. ”

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#### Annotation 1755896745228

 I recognized two life-changing principles early on, and I ’ m now handing them to you: Principle #1: The better the deal, the less people focused on me and the more they focus on getting that deal. If I had a clear winner on my hands, they really could not care less that I was an inexperienced investor. They just wanted the deal. Principle #2: Real estate is an inefﬁcient market. That means bad, good, and great deals are being generated all the time, and they pop up in unexpected places.

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#### Annotation 1755899366668

 On any given day, hundreds of busi- ness situations change in your town: Companies merge, expand, and decide to relocate. Contracts are awarded, marketing campaigns take off, and products get publicity. Other companies change hands because the owner dies or retires. These events often result in a property being put up for sale.

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#### Annotation 1755901988108

1. The Roles of Financial Reporting and Financial Statement Analysis
 The role of financial reporting is to provide information about a company's financial position and performance for use by parties both internal and external to the company. Financial statements are issued by management, who is responsible for their form and content. The role of financial statement analysis, on the other hand, is to take these financial statements and other information to evaluate the company's past, current, and prospective financial position and performance for the purpose of making rational investment, credit, and similar decisions. The primary users of financial statements are equity investors and creditors.
• Equity investors are primarily interested in the company's long-term earning power, growth, and ability to pay dividends.

• Short-term creditors (e.g., banks and trade creditors) are more interested in the company's immediate liquidity, because they seek an early payback of their investment.

• Long-term creditors (e.g., corporate bond owners such as insurance companies and pension funds) are primarily concerned with the company's long-term asset position and earning power.

#### Annotation 1755904871692

Subject 2. Major Financial Statements
 Financial statements are the most important outcome of the accounting system. They communicate financial information gathered and processed in the company's accounting system to parties outside the business. The four principal financial statements are:
• Income statement (statement of earnings)

• Balance sheet (statement of financial position)

• Cash flow statement

• Statement of changes in owners' or stockholders' equity

These four financial statements, augmented by footnotes and supplementary data, are interrelated. In addition, there are other sources of financial information, such as management discussion and analysis, auditor's reports, etc.

Income Statement

The income statement summarizes revenues earned and expenses incurred, and thus measures the success of business operations for a given period of time. It explains some but not all of the changes in the assets, liabilities, and equity of the company between two consecutive balance sheet dates.

The income statement lists income and expenses as they are directly related to the company's recurring income. The format of the income statement is not specified by U.S. GAAP and actual format varies across companies. The following is a generic sample:

The goal of income statement analysis is to derive an effective measure of future earnings and cash flows. Analysts need data with predictive ability, hence income from continuing (recurring) operations is considered to be the best indicator of future earnings. As operating expenses do not include financing costs such as interest expenses, operating income (EBIT) is independent of the company's capital structure.

In the typical income statement this means segregating the results of normal, recurring operations from the effects of nonrecurring or extraordinary items to improve the forecasting of future earnings and cash flows. The idea here is that recurring income is persistent. If an item in the unusual or infrequent component of income from continuing operations is deemed not to be persistent, then recurring (pre-tax) income from continuing operations should be adjusted.

The net income figure is used to prepare the statement of retained earnings.

Balance Sheet

A balance sheet provides a "snapshot" of a company's financial condition. Think of the balance sheet as a photo of the business at a specific point in time. It reports major classes and amounts of assets, liabilities, stockholders' equity, and their interrelationships as of a specific date.

Assets = Liabilities + Stockholders' Equity

• Assets are the economic resources controlled by the company.

• Liabilities are the financial obligations that the company must fulfill in the future.

Liabilities are typically fulfilled by payment of cash. They represent the source of

financing provided to the company by the creditors.

• Equity ownership is the owner's investments and the total earnings retained from

the commencement of the company. Equity represents the source of financing provided to the company by the owners.

Cash Flow Statement

The primary purpose of the cash flow statement is to provide information about a company's cash receipts and cash payments during a period. It reports the cash receipts and cash outflows classified according to operating, investment, and financing activities.

The cash flow statement is useful because it provides answers to the following simple yet important questions:

• Where did the cash come from during the period?

• What was the cash used for during the period?

• What was the change in the cash balance during the period?

The stat

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#### Annotation 1755906968844

 Subject 3. Other Financial Information Sources #reading-megafono Financial Notes and Supplementary Schedules Financial footnotes are an integral part of financial statements. They provide information about the accounting methods, assumptions and estimates used by management to develop the data reported in the financial statements. They provide additional disclosure in such areas as fixed assets, inventory methods, income taxes, pensions, debt, contingencies such as lawsuits, sales to related parties, etc. They are designed to allow users to improve assessments of the amounts, timing, and uncertainty of the estimates reported in the financial statements. Supplementary Schedules: In some cases additional information about the assets and liabilities of a company is provided as supplementary data outside the financial statements. Examples include oil and gas reserves reported by oil and gas companies, the impact of changing prices, sales revenue, operating income, and other information for major business segments. Some of the supplementary data is unaudited. Management Discussion and Analysis (MD&A) This requires management to discuss specific issues on the financial statements, and to assess the company's current financial condition, liquidity, and its planned capital expenditure for the next year. An analyst should look for specific concise disclosure as well as consistency with footnote disclosure. Note that the MD&A section is not audited and is for public companies only. Auditor's Reports See next subject for details. Other Sources of Information Interim reports. Publicly held companies must file form 10-Q (interim report) on a quarterly basis. It is far less detailed than annual financial statements, as it contains unaudited basic financial statements, unaudited footnotes to financial statements, and management discussion and analysis. Proxy statements. An analyst should look for litigation, executive compensation, and related-party transactions, known as proxy statements. Proxy statements should be considered an integral part of the financial report, and they may contain special compensation "perks" for officers and directors, as well as lawsuits and other contingent obligations facing the company. Companies' websites, press releases, and conference calls.

#### Annotation 1755907493132

 Follow the system for attracting deals, two things will happen: You’ll see a lot of worthless deals, and every so often you’ll come across a real gem.

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#### Annotation 1755910376716

Subject 4. Auditor's Reports
 The auditor (an independent certified public accountant) is responsible for seeing that the financial statements issued comply with generally accepted accounting principles. In contrast, the company's management is responsible for the preparation of the financial statements. The auditor must agree that management's choice of accounting principles is appropriate and that any estimates are reasonable. The auditor also examines the company's accounting and internal control systems, confirms assets and liabilities, and generally tries to be sure that there are no material errors in the financial statements. Though hired by the management, the auditor is supposed to be independent and to serve the stockholders and the other users of the financial statements. An auditor's report (also called the auditor's opinion) is issued as part of a company's audited financial report. It tells the end-user the following:
• Whether the financial statements are presented in accordance with generally accepted accounting principles.

• It identifies those circumstances in which such principles have not been consistently observed in the current period in relation to the preceding period.

• Informative disclosures in the financial statements are to be regarded as reasonably adequate unless otherwise stated in the report.

An auditor's report is considered an essential tool when reporting financial information to end-users, particularly in business. Since many third-party users prefer or even require financial information to be certified by an independent external auditor, many auditees rely on auditor reports to certify their information in order to attract investors, obtain loans, and improve public appearance. Some have even stated that financial information without an auditor's report is "essentially worthless" for investing purposes.

The Types of Audit Reports

There are four common types of auditor's reports, each one representing a different situation encountered during the auditor's work. The four reports are as follows:

• An unqualified opinion report is issued by an auditor when the financial statements presented are free of material misstatements and are in accordance with GAAP, which, in other words, means that the company's financial condition, position, and operations are fairly presented in the financial statements. It is the best type of report an auditee may receive from an external auditor. It is regarded by many as the equivalent of a "clean bill of health" to a patient, which has led many to call it the "clean opinion."

• A qualified opinion report is issued when the auditor encountered one or two situations that did not comply with generally accepted accounting principles; however, the rest of the financial statements are fairly presented. This type of opinion is very similar to an unqualified or "clean opinion," but the report states that the financial statements are fairly presented with a certain exception which is otherwise misstated.

• An adverse opinion is issued when the auditor determines that the financial statements of an auditee are materially misstated and generally do not comply with GAAP. It is considered the opposite of an unqualified or clean opinion, essentially stating that the information contained to assess the auditee's financial position and results of operations is materially incorrect, unreliable, and inaccurate.

• A disclaimer of opinion, commonly referred to simply as a disclaimer, is issued when the auditor could not form, and consequently refuses to present, an opinion on the financial statements. This type of report is issued when the auditor tried to audit a company but could not complete the work due to various reasons and does not issue an opinion.

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#### Annotation 1755912998156

 Your marketing systems will eventually ﬁnd a gem that’s so good, no one will care that it’s your ﬁrst deal.

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#### Annotation 1755914571020

Subject 5. Financial Statement Analysis Framework
 The financial statement analysis framework provides steps that can be followed in any financial statement analysis project, including the following:
• Articulate the purpose and context of the analysis.

• Collect input data.

• Process data.

• Analyze / interpret the processed data.
Interpret the output to support a conclusion (e.g., a buy decision).

• Develop and communicate conclusions and recommendations. Communicate the conclusion or recommendation in an appropriate format.

What is the purpose of the analysis? Evaluating an equity or debt investment? Or issuing a credit rating?

The context needs to be defined clearly too: Who is the intended audience? What is the nature and content of the final report? What is the time frame? What is the budget?

Gather a company's financial data from financial statements and other sources described in Subject c (other financial information sources). Also gather information on the economy and industry to understand the environment in which the company operates.

Compute ratios or growth rates, prepare common-size financial statements, create charts, perform statistical analyses, make adjustments to financial statements, etc.

Periodic review is required to determine if the original conclusions and recommendations are still valid.

#### Annotation 1755916668172

 Commercial Real Estate Will Open Up a Huge Segment of Your Local Market That You Previously Avoided

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#### Annotation 1755919027468

 Conﬁning yourself to investing only in single-family homes is like looking at your town through a drinking straw. The whole town is there, but your view is incredibly narrow. Once you are comfortable with my systems for investing in commercial property, you’ll be throwing that straw away. Everywhere you look, you will see opportunities that never occurred to you before. You will have become a transaction engineer.

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#### Annotation 1755926367500

 Maybe there is a parcel of land next to a highway where you can now envision a small ofﬁ ce building or strip mall. You could buy the land and ﬂ ip it to a developer for a nice proﬁt.

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#### Annotation 1755929513228

 Maybe there is a run - down strip mall (several stores next to each other in a row) that you pass every day while driving to work. You notice that with some simple improvements this area could be getting much more business.

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#### Annotation 1755932658956

 The more property types you can invest in, the easier it will be to ﬁ nd a great opportunity.

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#### Annotation 1755934231820

 Start anywhere you like — but make sure that you start . You do want to be a transaction engineer, but you do not want to have analysis paraly- sis, where you never quite get around to making offers and doing deals.

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#### Annotation 1755935804684

 Build a low - cost team of professionals to do the heavy lifting.

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#### Annotation 1755938163980

 Less Competition: They’re Scared Off Because They Don’t Know

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#### Annotation 1755941047564

 Have the right marketing systems in place, you’ll be successful regardless of how much competition there is. Second, that’s all the more reason to branch out from single - family homes into commercial property, where there are fewer investors.

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#### Annotation 1755943406860

 There’s no need to stop investing in one type of property, once you know how to invest that way. Instead, you simply focus on one type while keeping your eyes open to all the other possibilities that come your way.

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#### Annotation 1755945766156

 The true lubricant business was steady cash ﬂ ow. It didn't matter how powerful my real estate engine was; without that cash ﬂow, the gears would grind to a halt.

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#### Annotation 1755948125452

 With even a single commercial property, you can look forward to a nice check being dropped into your mailbox every month like clockwork.

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#### Annotation 1755949698316

 At ﬁrst the checks may be smaller because your number - one priority is to cover the cash ﬂow needs of the property. You’ll have operating expenses that must be paid each month, and capital expenses (major repairs) that will come up from time to time.

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#### Annotation 1755953106188

 Your ﬁrst goal may be to accumulate enough positive cash ﬂ ow so that it equals what you are earning in your full - time job. Then you’ll have the option to quit that job and become a full - time investor.

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#### Annotation 1755955465484

 Cash ﬂow will indeed set you free. It will give you the conﬁdence and the ability to do the things in life that you couldn't do before.

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#### Annotation 1755960446220

 You Can Think Big But Still Start Very Small You ’ ve heard Donald Trump say it: “ If you ’ re going to think, you might as well think big. ”

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#### Annotation 1755962019084

 Commercial property has two very important characteristics: It allows you to get as big as your imagination will let you, but it also allows you to start as small as you like.

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#### Annotation 1755963591948

 Dreams without action are not impressive.

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#### Annotation 1755965164812

 Commercial property is the path from your dreams and modest initial actions all the way up to your ultimate ﬁ nancial goals.

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#### Annotation 1755966737676

 it ’ s actu- ally easier to own larger properties, because they can support a larger team to run them for you.

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#### Annotation 1755968310540

 n a commercial property, you ’ ll have several tenants, and even hundreds. You still may lose one, but the others will continue to pay rent. This cash ﬂ ow should cover most, if not all, of your mortgage payment. Each tenant is like a pillar supporting your investment.

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#### Annotation 1755969883404

 With some investments you simply try to buy low and sell high. Commercial real estate gives you a whole rainbow of opportunities to proﬁ t.

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#### Annotation 1755971456268

 This is where the real money is. Equity build - up happens in two ways. The ﬁ rst is through paying down the mortgage principal. You ’ ll have your tenants to thank for that, whether it ’ s a multi - family, ofﬁ ce, retail space, or another type of property.

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#### Annotation 1755973291276

 Each month they will give you a big slice of their income in the form of rent checks. You use a portion of that money to make the mort- gage payment. In one sense, your tenants go to work each morning to buy the building for you.

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#### Annotation 1755974864140

 Harry Helmsley. When asked why he began investing in commercial properties, Harry said, “ I always liked the idea that a group of people would pool their money together to pay off the mortgage on my building. I also liked the idea that they would give me extra money at the end of the month that I could use to reinvest, put into a savings account, or just have some fun with. ”

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#### Annotation 1755976437004

 The second way to get equity build - up is through appreciation. Over time, real estate values in most areas go up. Yes, appreciation is subject to cycles, but over the long term, the line on the graph trends upward. Some markets appreciate faster than others.

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#### Annotation 1755978009868

 Cash ﬂ ow may be the vital lubricant of your real estate machine, but appreciation is the giant engine. Cash ﬂ ow allows you to run your properties, quit your job, and start enjoying the ﬁ ner things in life. Appreciation comes more slowly, but has the potential to add many zeros to your bank account.

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#### Annotation 1755979582732

 #emerging #markets Real estate investing is my focus, but the study of emerging markets is my passion. At any given time — regardless of what the national economy is doing — there are markets around the United States that are just on the verge of explosive growth.

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#### Annotation 1755982204172

 There are two tricks to making money in emerging markets: First, you must be able to locate these markets slightly before most other investors know that they are good. Second, you must be willing to invest when other people think you ’ re crazy.

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#### Annotation 1756308311308

 you will be buying low , or investing when other peo- ple don ’ t see the value. That positions you to sell high — in other words, when other people think you ’ re crazy for selling too soon.

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#### Annotation 1756309884172

 There are emerging markets for commercial properties all around the United States at any given time.

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 different types of commercial property follow different paths in the market cycle. Simply because a market is emerging for apartments does not mean that it is emerging for retail space.

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#### Annotation 1756313029900

 retail space generally lags behind apartments:

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#### Annotation 1756314864908

 #emerging #markets First come the announcements that new job opportunities will be opening up in an area. That creates a demand for ofﬁ ce space.

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#### Annotation 1756317486348

 #emerging #markets Then the people who will work in those ofﬁ ces begin to move into town. Because homes can ’ t be built fast enough, the apartment market suddenly heats up.

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#### Annotation 1756319845644

 #emerging #markets Many people want to see if their job will work out, and they want to get a good feel for the community. They check things out by rent- ing ﬁ rst. After their leases expire, they start to buy single - family houses.

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#### Annotation 1756326399244

 IASB Goals #reading-agustin-rios The IASB has four stated goals: 1. Develop global accounting standards requiring transparency, comparability, and high quality in financial statements. 2. Promote the use of global accounting standards. 3. Account for the needs of emerging markets and small firms when implementing global accounting standards. 4. Achieve convergence between various national accounting standards and global accounting standards.

#### Annotation 1756328234252

 Retail space tends to follow housing surges, as merchants realize they can make money by moving closer to where people live and work.

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 Discovering how to recognize the signs of emerging markets — and then acting on that knowledge — will make you a very rich person.

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 Forced Appreciation This is one of the fastest ways to make money with commercial prop- erties. The concept is also called a value play . Whenever you look at a deal, always look for ways to force appreciation beyond what the local market may naturally generate.

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 To force appreciation, you must ﬁ nd a deal with a slight problem.

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 the previous owner. Maybe he ’ s been afraid to raise rents, so his rents are under market. Maybe he is charging the correct amount for rent, but has higher - than - normal vacancies. Perhaps his expenses are running high. These are all opportunities to buy a property with a built - in reward, as long as you buy based on the actual numbers . That is the key to buying right with commercial properties.

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 Most sellers try to sell based on projected or pro forma numbers. This means that they are basing their price on what they think you can earn after you buy the property. The problem with pro forma numbers is they are not real. You are buying based on future cash ﬂ ows that may never materialize.