on 25-Apr-2018 (Wed)

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

Annotation 1803137977612

 #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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Annotation 1803139550476

 #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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Annotation 1803141123340

 #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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Annotation 1803142696204

 #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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Annotation 1803144269068

 #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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Annotation 1803145841932

 #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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Annotation 1803147414796

 #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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Annotation 1803148987660

 #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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Annotation 1803150560524

 #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.
a cedilla

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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.
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.
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 [...].
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.
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.
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.
-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.
-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.
-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.
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.
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.

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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

Annotation 1803186736396

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

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Annotation 1803188309260

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

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Annotation 1803189882124

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

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Annotation 1803191454988

 #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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Annotation 1803193027852

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

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Flashcard 1803209280780

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

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Flashcard 1803211115788

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

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Flashcard 1803212950796

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

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Flashcard 1803214785804

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

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Flashcard 1803217145100

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

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Flashcard 1803218980108

Tags
#has-images #jaynes #plausible-reasoning
[unknown IMAGE 1803207970060]
Question
In Boolean logic, the implication proposition can be represented as logical equation of [...]
[unknown IMAGE 1803206397196]

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Flashcard 1803221601548

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

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Flashcard 1803234184460

Tags
#jaynes #plausible-reasoning
Question
the logical product denotes the proposition ‘[...]
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 [...]
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
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 [...]
reciprocal

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The relation between a proposition and its denial is reciprocal

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Flashcard 1803243621644

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

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Annotation 1803245456652

 #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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Annotation 1803247029516

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

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Annotation 1803249126668

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

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Annotation 1803250699532

 #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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Annotation 1803252272396

 #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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Annotation 1803253845260

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

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Annotation 1803255418124

 #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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Annotation 1803256990988

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

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Annotation 1803258563852

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

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Annotation 1803261709580

 #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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Annotation 1803263282444

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

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Annotation 1803264855308

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

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Annotation 1803266428172

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

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Annotation 1803268001036

 #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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Annotation 1803272719628

 #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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Annotation 1803274292492

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

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Annotation 1803275865356

 #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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Annotation 1803277438220

 #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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Annotation 1803279011084

 #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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Annotation 1803280583948

 #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

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

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The theory of plausible reasoning is based on weak syllogisms

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Flashcard 1803285302540

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

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

Tags
#jaynes #plausible-reasoning
Question
[...] implies all propositions
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

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

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

Tags
#jaynes #plausible-reasoning
Question
logic functions with only one point being true can be constructed simply by [...],
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

Tags
#jaynes #plausible-reasoning
Question
Any logic function that is true on at least one point can be constructed as [...]
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

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

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

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Flashcard 1803303390476

Tags
#jaynes #plausible-reasoning
Question
the operation NOR defined by [...]
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
(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
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

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

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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 [...]
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

Tags
#jaynes #plausible-reasoning
Question
We expect plausible reasoning to have no [...] and be able to determine 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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#jaynes #plausible-reasoning
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We expect plausible reasoning to have no contradictions and be able to determine the plausibility of [...]
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
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A ⇒ B is false only if [...]
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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The question of [...] arises in a crucial way in the Gödel theorem
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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#jaynes #plausible-reasoning
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The duality property shows [...] is the same as denying that they are both false $$\overline{ \bar{A} \bar{B} }$$
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
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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
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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#jaynes #plausible-reasoning
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Saying at least one proposition is true $$A + B$$ is the same as [...]
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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Annotation 1803339304204

 [unknown IMAGE limites_de_tiempo_de_aspiracion]