Chapitre 1. Intro

P Q
P Q P Q P ⇒Q P ⇔Q P ⇒(Q R)
(1 = 2) ⇒(3 = 4)
A B C
A(B C)⇐⇒ (A B) (A C)
x
(x−1)(x−2) = 0
x(2x+ 1) = 0
⇒
x
x2≥1
x2≥1

P(x, y)x y
∀x∈Rx2> x
∀x∈R(x2=−1) ⇒(x2= 7)
∀x∈R∃y∈Ry2=x
∀x∈R(∃y∈Ry2=x)⇒x≥0
∃m∈N(m6= 1 m6= 4
∀z∈C(z= ¯z)⇔(z∈R)
P1:∀n∈N∃M∈Nn≤M
P1P1
P2:∃M∈N∀n∈Nn≤M
(un)n∈N
(un)n∈N(un)n∈N(un)n∈N
(un)n∈N(un)n∈N
n n2n
√2
√3
p√p

7x1x7
7
X
i=1
xi= 0
i xi≤0
a  > 0|a| ≤ 
a= 0
a b  > 0a≤b+
a≤b
n2nn!
n≥1
n
X
k=1
k2=n(n+ 1)(2n+ 1)
6
f:R→R
f
∀x≥0f(x)≥0
f
x f(x)≥1f(x)≤ −1
E F E ×F
A×B A ⊂E B ⊂F
A B C
E
(A∪B)c=Ac∩Bc
(A∩B)c=Ac∪Bc
A∩B=A⇐⇒ A⊂B
A∪B=B⇐⇒ A⊂B
A∪(B−A) = A∪B
(A−B)−C=A−(B∪C)

f:E→F E F A B
E
f(A∪B) = f(A)∪f(B)
f(A∩B) = f(A)∩f(B)
E F G f :E→F g :F→G
g◦f f
g◦f g
g:Z×N∗→Qf(m, n) = m
n
g:Z×N∗→Qf(m, n) = m+1
n+ 1
f:N2→Rf(a, b) = a+b√2f
Z N
f:N2→Rf(a, b) = a+b√2f