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math prepa > Chapitre 4 : applications > Flashcards

Chapitre 4 : applications Flashcards

1
Q

definition de l’application

A
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2
Q

l’ensemble image

A
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3
Q

définition de deux applications égales

A
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4
Q

definition de l’application idendité

A
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5
Q

définition de l’image directe

A
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6
Q

Définition de la préimage ou de l’image réciproque

A
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7
Q

la restriction d’une implication

A
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8
Q

définition du prolongement d’une implication

A
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9
Q

definition de la composee gof

A
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10
Q

composée d’applications

A
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11
Q

definition ho(gof)

A
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12
Q

composee d’une application avec identité

A
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13
Q

definition de l’injection

A
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14
Q

la composée de deux injections

A

est une injection

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15
Q

definition de la surjectivité

A
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16
Q

application de E et F(E)

A
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17
Q

la composée de deux surjection s

A

est une surjection

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18
Q

definition de la bijection

A
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19
Q

f est bijective ssi

A

f est injective et bijective

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20
Q

la composée de deux bijections

A

est une bijection

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21
Q

si f est une application injective de E dans F , alors

A

elle réalise une bijection de E dans F(E)

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22
Q

F est fini et Card(E) = Card(F)

A

si f est une bijection de E dans F et si E est un ensemble fini

23
Q

theoreme sur une application qui est a la fois injective, surjective et bijective

A
24
Q

définition de l’application réciproque d’une bijection

A
25
Q

théorème différentes égalités entre une bijection et son application réciproque

A
26
Q

Théorème sur la reciproque fe la composée de bijection

A
27
Q

théorème de la bijection monotone

A
28
Q

théorème sur l’unique solution

A
29
Q
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30
Q
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31
Q
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32
Q
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33
Q
A
34
Q
A
35
Q

démonstration

A
36
Q
A
37
Q

démonstration

A
38
Q

démonstration

A
39
Q

démonstration

A
40
Q
A
41
Q
A
42
Q

démonstration

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43
Q

démonstration

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44
Q
A

d’apres th 11:
(gof)^-1 = f^-1 o g^-1

45
Q
A
46
Q
A
47
Q

f(E) =

A
48
Q
A
49
Q
A
50
Q

consequence

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51
Q

consequence

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52
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A
53
Q
A
54
Q
A

math prepa (10 decks)

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