Chapitre 0 – Ensembles de nombres

N
0
N∗
0
174 13 58721
Z
−174 13 −58721 0 17542
N⊂Z
Q
Q=np
q|p∈Z, q ∈N∗, P GCD(p, q)=1o
−174
523
13
2−58721 0 17542
Z⊂Q

n
n
1
R
−174
523 π0 17542
Q⊂R
√2√2∈R\Q
√2
p∈Zq∈N∗√2 = p
qP GCD(p, q)=1
√2 = p
q
(√2)2=p2
q2
2 = p2
q2
2q2=p2
p22p2p0∈Z
p= 2 ×p0
2q2=p2= (2p0)2= 4p02q2= 2p02q22
q2
p q 2P GCD(p, q)≥2
√2
N⊂Z⊂Q⊂R