Poly de F. Bories

E F

∈:/∈:
∀:∃:
⇒:⇐⇒ :
∪:∩:
⊂:∅:
∃!
P(E)E
E\A E
A E
{x∈E| P} x E P
E×F
n
Y
i=1
EiEn
(ai)i∈IE I
n
X
i=1
ai(ai)1≤i≤nE
n
Y
i=1
ai(ai)1≤i≤nE
n,p i n ≤i≤p n p
n≤p
∗=\{0},∗=\{0},∗=\{0},∗=\{0},∗=\{0}
n! =
n
Y
i=1
i n n 0! = 1
Ãn
p!=n! p!(n−p)! p n
f:E−→ F
x7−→ yE F x E
y F
f−1(A)f A F
f−1f
g◦f f g
idEE
(A) : A,
(A) : A,

n p n ≤p,
n,p ={i∈ | n≤i≤p}.
E F f E
F x E y,
f(x)F. y x f x
y.
f:E−→ F
x7−→ f(x)
E F
x E y F x y y =f(x).
E={1,2,3}, F ={a,b,c,d}, f f(1) = f(2) = a, f(3) = d.
*
*
j
1
2
3
a
b
c
d
x E f.
y F
A E, A f F :
f(A) = {y∈F| ∃x∈A:f(x) = y}.
f(E)f.
B F B f
E:
f−1(B) = {x∈E|f(x)∈B}.

f E F
∀x∈E, ∀x0∈E, f(x) = f(x0)⇒x=x0.
∀x∈E, ∀x0∈E, x 6=x0⇒f(x)6=f(x0).
F
f E F
∀y∈F, ∃x∈E:y=f(x).
f=F.
F
f E F
∀y∈F, ∃!x∈E:y=f(x).
F
F E,
f f−1. f−1
x=f−1(y)⇐⇒ y=f(x).
F,
f E F
f f
f:E−→ F
g:E0−→ F0
E E0F F 0
h:E∪E0−→ F∪F0
si x∈E, h(x) = f(x),
si x∈E0, h(x) = g(x).
h f g
h f g
h f g

f g x x0E∪E0,
h(x) = h(x0).
x E x0E0h(x) = f(x),
F h(x0) = g(x0), F 0. h(x) = h(x0)
F F 0
x x0E, f(x) = f(x0)x x0
E0, g(x) = g(x0). x =x0.
h
h x x0E,
f(x) = f(x0). h(x) = h(x0), x =x0.
f g
h h =F∪F0.
h=f∪g. F F 0
f g.
h=F∪F0⇐⇒ (f=F g =F0).
f:E−→ F g :F−→ G.
f g g ◦f
h:E−→ G
x7−→ g(f(x))
f g
(g◦f)−1=f−1◦g−1.