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Flashcard 1802553396492

Tags
#topology
Question
any affine transformation is equivalent to a [...] followed by a translation.


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any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation.

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Affine transformation - Wikipedia
es in Euclidean spaces, each output coordinate of an affine map is a linear function (in the sense of calculus) of all input coordinates. Another way to deal with affine transformations systematically is to select a point as the origin; then, <span>any affine transformation is equivalent to a linear transformation (of position vectors) followed by a translation. Contents [hide] 1 Mathematical definition 1.1 Alternative definition 2 Representation 2.1 Augmented matrix 2.1.1 Example augmented matrix 3 Properties 3.1 Properti







#french #verbs
Verbs ending in -cer add a cedilla to the c before the letters a or o in order to retain the soft c sound. avancer to advance nous avanc¸ ons

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#french #verbs
Verbs ending in -ger add an e after the g before the letters a and o in order to maintain the soft g sound. changer to change nous changeons

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#french #verbs
Verbs which have -é- in the penultimate syllable of the infinitive change -é- to -è- in all forms except the nous and vous forms.

compléter: je complète; tu complètes; il, elle, on complète; nous complétons; vous complétez; ils, elles complètent

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#french #verbs
In some verbs which contain -e- in the next to the last syllable of the infinitive, the -e- changes to -e ` - in all forms except the nous and vous forms. Study the following. lever je le ` ve tu le ` ves il, elle, on le ` ve nous levons vous levez ils, elles le ` vent

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#french #verbs
In other verbs with -e- in the infinitive, the final consonant is doubled in all but the nous and vous forms.

jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent

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#french #verbs
Verbs whose infinitive ends in -oyer, -uyer and -ayer change -y- to -i- in all but the nous and vous forms.

nettoyer: je nettoie; tu nettoies; il, elle, on nettoie; nous nettoyons; vous nettoyez; ils, elles nettoient

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#french #verbs
Verbs whose infinitive ends in -ir add -is, -is, -it, -issons, -issez, -issent to the stem.

finir: je finis; tu finis; il, elle, on finit; nous finissons; vous finissez; ils, elles finissent

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#french #verbs
Verbs whose infinitive ends in -re add -s, -s, -, -ons, -ez, -ent to the stem.

répondre: je réponds; tu réponds; il, elle, on répond; nous répondons; vous répondez; ils, elles répondent

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#french #verbs
Some verbs like ouvrir, offrir, and cueillir, although the infinitive ends in -ir, are conjugated like regular -er verbs.

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Flashcard 1803152133388

Tags
#french #verbs
Question
Verbs ending in -cer add [...] to the c before the letters a or o in order to retain the soft c sound.
Answer
a cedilla

avancer to advance, nous avançons


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Verbs ending in -cer add a cedilla to the c before the letters a or o in order to retain the soft c sound. avancer to advance nous avanc¸ ons

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Flashcard 1803154492684

Tags
#french #verbs
Question
Verbs ending in -ger add [...] after the g before the letters a and o in order to maintain the soft g sound.
Answer
an e

changer to change, nous changeons


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Verbs ending in -ger add an e after the g before the letters a and o in order to maintain the soft g sound. changer to change nous changeons

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Flashcard 1803157638412

Tags
#french #verbs
Question
Verbs which have -é- in [...] of the infinitive change -é- to -è- in all forms except the nous and vous forms.
Answer
the penultimate syllable

compléter: je complète; tu complètes; il, elle, on complète; nous complétons; vous complétez; ils, elles complètent
The two are pronounced differently:
é[e]café [kafe]
è[ɛ]père [père]


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Verbs which have -é- in the penultimate syllable of the infinitive change -é- to -è- in all forms except the nous and vous forms. compléter : je complète; tu complètes; il, elle, on complète; nous complétons; vous compléte

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Flashcard 1803159997708

Tags
#french #verbs
Question
Verbs which have -é- in the penultimate syllable of the infinitive change -é- to -è- in all forms except [...].
Answer
the nous and vous forms

compléter: je complète; tu complètes; il, elle, on complète; nous complétons; vous complétez; ils, elles complètent
The changes are used to indicate the stress of the word; the nous and vous don't change because they already have their stress


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Verbs which have -é- in the penultimate syllable of the infinitive change -é- to -è- in all forms except the nous and vous forms. compléter : je complète; tu complètes; il, elle, on complète; nous complétons; vous complétez; ils, elles complètent

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Flashcard 1803163143436

Tags
#french #verbs
Question
In other verbs with -e- in the infinitive, [...] is doubled in all but the nous and vous forms.
Answer
the final consonant

jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent


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In other verbs with -e- in the infinitive, the final consonant is doubled in all but the nous and vous forms. jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent

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Flashcard 1803165502732

Tags
#french #verbs
Question
In other verbs with -e- in the infinitive, the final consonant is doubled in all but [...] forms.
Answer
the nous and vous

jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent
These are the shorter words, one syllable.


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In other verbs with -e- in the infinitive, the final consonant is doubled in all but the nous and vous forms. jeter: je jette; tu jettes; il, elle, on jette; nous jetons; vous jetez; ils, elles jettent

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Flashcard 1803169434892

Tags
#french #verbs
Question
Verbs whose infinitive ends in [...] change -y- to -i- in all but the nous and vous forms.
Answer
-oyer, -uyer and -ayer

nettoyer: je nettoie; tu nettoies; il, elle, on nettoie; nous nettoyons; vous nettoyez; ils, elles nettoient
This change avoids adding unnecessary trailing sound to the verbs


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Verbs whose infinitive ends in -oyer, -uyer and -ayer change -y- to -i- in all but the nous and vous forms. nettoyer: je nettoie; tu nettoies; il, elle, on nettoie; nous nettoyons; vous nettoyez; ils, elles nettoient

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Flashcard 1803172580620

Tags
#french #verbs
Question
In present tense, verbs whose infinitive ends in -ir add [...] to the stem.
Answer
-is, -is, -it, -issons, -issez, -issent

finir: je finis; tu finis; il, elle, on finit; nous finissons; vous finissez; ils, elles finissent


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Verbs whose infinitive ends in -ir add -is, -is, -it, -issons, -issez, -issent to the stem. finir : je finis; tu finis; il, elle, on finit; nous finissons; vous finissez; ils, elles finissent

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Flashcard 1803175726348

Tags
#french #verbs
Question
Verbs whose infinitive ends in -re add [...] to the stem.
Answer
-s, -s, -, -ons, -ez, -ent

répondre: je réponds; tu réponds; il, elle, on répond; nous répondons; vous répondez; ils, elles répondent


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Verbs whose infinitive ends in -re add -s, -s, -, -ons, -ez, -ent to the stem. répondre : je réponds; tu réponds; il, elle, on répond; nous répondons; vous répondez; ils, elles répondent

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Flashcard 1803179134220

Tags
#french #verbs
Question
Some verbs like [...], although the infinitive ends in -ir, are conjugated like regular -er verbs.
Answer
ouvrir, offrir, and cueillir


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Some verbs like ouvrir , offrir , and cueillir , although the infinitive ends in -ir, are conjugated like regular -er verbs.

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Flashcard 1803180707084

Tags
#french #verbs
Question
Some verbs like ouvrir, offrir, and cueillir, although the infinitive ends in -ir, are conjugated like [...] verbs.
Answer
regular -er


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Some verbs like ouvrir , offrir , and cueillir , although the infinitive ends in -ir, are conjugated like regular -er verbs.

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Flashcard 1803183066380

Tags
#functional-analysis
Question
Functional analysis studies
  1. [...] that are endowed with some kind of limit-related structure and
  2. the linear functions defined on these spaces and respecting these structures in a suitable sense.
Answer


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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, et

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Functional analysis - Wikipedia
analysis (psychology). [imagelink] One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. <span>Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that







Flashcard 1803183590668

Tags
#functional-analysis
Question
Functional analysis studies
  1. vector spaces that are endowed with some kind of limit-related structure and
  2. the [...] defined on these spaces and respecting these structures in a suitable sense.


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Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, et

Original toplevel document

Functional analysis - Wikipedia
analysis (psychology). [imagelink] One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. <span>Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word functional goes back to the calculus of variations, implying a function whose argument is a function and the name was first used in Hadamard's 1910 book on that







#jaynes #plausible-reasoning
the logical product or the conjunction, denotes the proposition ‘both A and B are true

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#jaynes #plausible-reasoning
the logical sum or disjunction, stands for ‘at least one of the propositions, A, B is true’

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#jaynes #plausible-reasoning
These symbols are only a shorthand way of writing propositions, and do not stand for numerical values

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#jaynes #plausible-reasoning
that A and B have the same truth value, then they are logically equivalent propositions, in the sense that any evidence concerning the truth of one pertains equally well to the truth of the other, and they have the same implications for any further reasoning

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#jaynes #plausible-reasoning
The relation between a proposition and its denial is reciprocal

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Flashcard 1803209280780

[unknown IMAGE 1803198532876]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the idempotence property means [...]


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Flashcard 1803211115788

[unknown IMAGE 1803200105740]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the commutativity property means [...]


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Flashcard 1803212950796

[unknown IMAGE 1803201678604]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the associativity property means [...]


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Flashcard 1803214785804

[unknown IMAGE 1803203251468]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the distributivity property means [...]


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Flashcard 1803217145100

[unknown IMAGE 1803204824332]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the duality property means [...]
Answer
Compare it to the De Morgan's law in set theory


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Flashcard 1803218980108

[unknown IMAGE 1803207970060]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the implication proposition can be represented as logical equation of [...]


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Flashcard 1803221601548

[unknown IMAGE 1803207970060]
Tags
#has-images #jaynes #plausible-reasoning
Question
In Boolean logic, the implication proposition means [...] is true or equally [...] is false
Answer
\(\overline{A} + B\), \(A \overline{B}\)


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Flashcard 1803234184460

Tags
#jaynes #plausible-reasoning
Question
the logical product denotes the proposition ‘[...]
Answer
both A and B are true


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the logical product or the conjunction, denotes the proposition ‘both A and B are true

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Flashcard 1803236543756

Tags
#jaynes #plausible-reasoning
Question
the logical sum stands for [...]
Answer
at least one of A, B is true


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the logical sum or disjunction, stands for ‘at least one of the propositions, A, B is true’

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Flashcard 1803238903052

Tags
#jaynes #plausible-reasoning
Question
propositions with the same truth value are [...] propositions
Answer
logically equivalent


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that A and B have the same truth value, then they are logically equivalent propositions, in the sense that any evidence concerning the truth of one pertains equally well to the truth of the other, and they have the same implications for any further reasoning

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Flashcard 1803242048780

Tags
#jaynes #plausible-reasoning
Question
The relation between a proposition and its denial is [...]
Answer
reciprocal


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The relation between a proposition and its denial is reciprocal

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Flashcard 1803243621644

[unknown IMAGE 1803207970060]
Tags
#has-images #jaynes #plausible-reasoning
Question
the strong syllogisms can be represented in Boolean logic as [...]


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#jaynes #plausible-reasoning
The theory of plausible reasoning based on weak syllogisms is not a ‘weakened’ form of logic; it is an extension of logic with new content not present at all in conventional deductive logic.

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#jaynes #plausible-reasoning
a false proposition implies all propositions

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#jaynes #plausible-reasoning
merely knowing the truth values of propositions A and B does not provide any information on deducibility

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#jaynes #plausible-reasoning
An expression B = f (A 1 ,...,A n ) involving n propositions is a logic function on a space S of M = 2 n points; and there are exactly 2 M such functions.

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#jaynes #plausible-reasoning
Since we are, at this stage, restricting our attention to Aristotelian propositions, any logic function C = f (A, B) such as (1.15) has only two possible ‘values’, true and false; and likewise the ‘independent v ariables’ A and B can take on only those two values.

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#jaynes #plausible-reasoning
logic functions with only one point being true can be constructed simply by conjunctions of input propositions,

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#jaynes #plausible-reasoning
Any logic function that is true on at least one point can be constructed as logical sum of basic conjunctions

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#jaynes #plausible-reasoning
the two operations (AND, NOT) already constitute an adequate set for deductive logic

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#jaynes #plausible-reasoning
A set of operations suffice to generate all possible logic functions form an adequate set

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#jaynes #plausible-reasoning
The duality property shows the logic disjunction \( A + B \) is the same as denying that they are both false \( \overline{ \bar{A} \bar{B} } \)

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#jaynes #plausible-reasoning
The operation ‘NAND’ is defined as the negation of ‘AND’

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#jaynes #plausible-reasoning
the operation NOR defined by the negation of OR

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#jaynes #plausible-reasoning
besides a common ground, a logic gate has two input terminals and one output

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#jaynes #plausible-reasoning
We call them ‘desiderata’ rather than ‘axioms’ because they do not assert that anything is ‘true’ but only state what appear to be desirable goals.

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#jaynes #plausible-reasoning
We expect plausible reasoning to have no contradictions and be able to determine any unique extension of logic

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#jaynes #plausible-reasoning
A ⇒ B is false only if A is true and B is false

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#jaynes #plausible-reasoning
The question of logical deducibility of one proposition from a set of others arises in a crucial way in the Gödel theorem

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#jaynes #plausible-reasoning
This great difference in the meaning of the word implies in ordinary language and in formal logic is a tricky point that can lead to serious error if it is not properly understood

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#jaynes #plausible-reasoning
The theory of plausible reasoning is based on weak syllogisms

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The theory of plausible reasoning based on weak syllogisms is not a ‘weakened’ form of logic; it is an extension of logic with new content not present at all in conventional deductive logic.

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#jaynes #plausible-reasoning
Plausible reasoning is an extension of deductive logic because it also applies to weak syllogisms.

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The theory of plausible reasoning based on weak syllogisms is not a ‘weakened’ form of logic; it is an extension of logic with new content not present at all in conventional deductive logic.

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Flashcard 1803283729676

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#jaynes #plausible-reasoning
Question
The theory of plausible reasoning is based on [...]
Answer
weak syllogisms


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The theory of plausible reasoning is based on weak syllogisms

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Flashcard 1803285302540

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#jaynes #plausible-reasoning
Question
Plausible reasoning is an extension of [...] because it also applies to weak syllogisms.
Answer
deductive logic


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Plausible reasoning is an extension of deductive logic because it also applies to weak syllogisms.

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Flashcard 1803286875404

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#jaynes #plausible-reasoning
Question
[...] is an extension of deductive logic because it also applies to weak syllogisms.
Answer
Plausible reasoning


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Plausible reasoning is an extension of deductive logic because it also applies to weak syllogisms.

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Flashcard 1803288448268

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#jaynes #plausible-reasoning
Question
[...] implies all propositions
Answer
a false proposition

If a proposition \( A \) is false, then \( A \) and \( A B \) always have the same truth value


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a false proposition implies all propositions

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Flashcard 1803291593996

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#jaynes #plausible-reasoning
Question
merely knowing the truth values of propositions A and B does not provide any information on [...]
Answer
deducibility


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merely knowing the truth values of propositions A and B does not provide any information on deducibility

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Flashcard 1803293166860

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#jaynes #plausible-reasoning
Question
merely knowing the [...] of propositions A and B does not provide any information on deducibility
Answer
truth values


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merely knowing the truth values of propositions A and B does not provide any information on deducibility

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Flashcard 1803295526156

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#jaynes #plausible-reasoning
Question
logic functions with only one point being true can be constructed simply by [...],
Answer
conjunctions of input propositions


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logic functions with only one point being true can be constructed simply by conjunctions of input propositions,

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Flashcard 1803297885452

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#jaynes #plausible-reasoning
Question
Any logic function that is true on at least one point can be constructed as [...]
Answer
logical sum of basic conjunctions


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Any logic function that is true on at least one point can be constructed as logical sum of basic conjunctions

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Flashcard 1803301031180

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#jaynes #plausible-reasoning
Question
The operation ‘NAND’ is defined as [...]
Answer
the negation of ‘AND’


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The operation ‘NAND’ is defined as the negation of ‘AND’

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Flashcard 1803303390476

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#jaynes #plausible-reasoning
Question
the operation NOR defined by [...]
Answer
the negation of OR


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the operation NOR defined by the negation of OR

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Flashcard 1803305749772

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#jaynes #plausible-reasoning
Question
the two operations [...] already constitute an adequate set for deductive logic
Answer
(AND, NOT)


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the two operations (AND, NOT) already constitute an adequate set for deductive logic

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Flashcard 1803307322636

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#jaynes #plausible-reasoning
Question
A set of operations suffice to [...] form an adequate set
Answer
generate all possible logic functions


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A set of operations suffice to generate all possible logic functions form an adequate set

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Flashcard 1803308895500

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#jaynes #plausible-reasoning
Question
the two operations (AND, NOT) already constitute an adequate set for [...]
Answer
deductive logic


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the two operations (AND, NOT) already constitute an adequate set for deductive logic

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Flashcard 1803310468364

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#jaynes #plausible-reasoning
Question
A set of operations suffice to generate all possible logic functions form an [...]
Answer
adequate set


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A set of operations suffice to generate all possible logic functions form an adequate set

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Flashcard 1803314400524

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#jaynes #plausible-reasoning
Question
besides a common ground, a logic gate has [...]
Answer
two input terminals and one output


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besides a common ground, a logic gate has two input terminals and one output

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Flashcard 1803316759820

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#jaynes #plausible-reasoning
Question
We expect plausible reasoning to have no [...] and be able to determine any unique extension of logic
Answer
contradictions


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We expect plausible reasoning to have no contradictions and be able to determine any unique extension of logic

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Flashcard 1803318332684

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#jaynes #plausible-reasoning
Question
We expect plausible reasoning to have no contradictions and be able to determine the plausibility of [...]
Answer
any unique extension of logic


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We expect plausible reasoning to have no contradictions and be able to determine any unique extension of logic

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Flashcard 1803319905548

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#jaynes #plausible-reasoning
Question
A ⇒ B is false only if [...]
Answer
A is true and B is false


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A ⇒ B is false only if A is true and B is false

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Flashcard 1803323051276

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#jaynes #plausible-reasoning
Question
The question of [...] arises in a crucial way in the Gödel theorem
Answer
logical deducibility of one proposition from a set of others


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The question of logical deducibility of one proposition from a set of others arises in a crucial way in the Gödel theorem

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Flashcard 1803324886284

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#jaynes #plausible-reasoning
Question
The duality property shows [...] is the same as denying that they are both false \( \overline{ \bar{A} \bar{B} } \)
Answer
the logic disjunction \( A + B \)


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The duality property shows the logic disjunction A+B is the same as denying that they are both false A¯B¯⎯⎯⎯⎯⎯⎯⎯

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Flashcard 1803327245580

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#jaynes #plausible-reasoning
Question
This great difference in the meaning of the word [...] in ordinary language and in formal logic is a tricky point that can lead to serious error if it is not properly understood
Answer
implies


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This great difference in the meaning of the word implies in ordinary language and in formal logic is a tricky point that can lead to serious error if it is not properly understood

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Flashcard 1803328818444

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#jaynes #plausible-reasoning
Question
Saying at least one proposition is true \( A + B \) is the same as [...]
Answer
denying both are false \( \overline{ \bar{A} \bar{B} } \)

The duality property


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The duality property shows the logic disjunction A+B is the same as denying that they are both false A¯B¯⎯⎯⎯⎯⎯⎯⎯

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