Sous-groupes de R

α β β 6= 0
n=α
βα−nβ ∈[0, β[
(n, ρ)∈N×[0, β[α=nβ +ρ
G6={0}(R,+) a= (G∩]0,+∞[)
a∈]0,+∞[G=QG=D
G=Z
a > 0G={na/n ∈Z}=aZ
a= 0 GR
a < b g ∈G0< g < b −a
exp(G) (R+∗,×)
H(R+∗,×)−1 exp(H)
(R,+)
(R+∗,×)
x y Z[x, y] = {nx +my/(n, m)∈Z2}
Z[x, y]R
x
y=p q(p, q)∈Z×N∗
p q
a=x
p=y qZ[x, y]⊂aZ
Z[x, y] = aZ
Z1
3,1 5
x
yZ[x, y]R
f:R→RT T 0
T
T0P∈R∗
f P
f
α{mα − bmαc/m ∈N}[0,1]
Z[α, −1]
f:R→RT
α
T{f(mα)/m ∈N}
f(R)
r(cos(rn))n∈N(sin(rn))n∈N
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ρ ρ1
ρ−ρ1∈]−β, β[
G∩]0,+∞[
aZ⊂G x ∈G
a
]a, b[6=∅b−a > 0g < b −a g ∈G
G]a, b[
−1
exp(H)
(R,+)
(R+∗,×)
Z[x, y]
a∈Z[x, y]
a
Z[x, y]aZ
fZ[T, T 0]
PZ[T, T 0] = PZT
T0
P∈R∗f P
fZ[T, T 0]
f
]a, b[⊂[0,1] Z[α, −1]
Extrait gratuit de document, le document original comporte 6 pages.