Corrigé du QCM 3 1. Pour tout j ∈ N , on munit l`intervalle Xj := [−j, j

j∈NXj:= [−j, j]Tj
RX:= Qj∈NXj
T=Qj∈NTjj∈NTj
T2
2
j∈NXj
RTjXj
T
j∈NXj:= [−j, j]Tj
RX:= Qj∈NXj
T=Qj∈NTjx∈X
x= (xj)j∈N
2Qj∈N]0, j[T
2p5:X−→ [−5,5] x x5
Qj∈N]0, j[
p5
Q⊂RxRy y −x∈Q
RΠR:R−→ R/Q
x∈R˜x∈R/Q
R/Q
2R/Q
2{˜ 0} ≡ ΠR(0)R/Q
√2
˜
√2 := √2 + p
q;p∈Z, q ∈N∗˜
0 := p
q;p∈Z, q ∈N∗≡Q
R/Q
ΠR(0)R/QΠ−1
RΠR(0) ≡Q
R

R∗≡(R\ {0})R
2A:=]0,1[∩(R\Q)R
2R R∗≡(R\ {0})
R
A A = (α, β)A
√2/4π/4
0≤α < β ≤1 ]α, β[A
R]− ∞,+∞[
R∗R∗
−
R∗R∗
−R∗
R∗]− ∞,0[ R
R∗R∗]− ∞,0] R
fR R∗
f(R) = R∗fR