V. Bansaye_540.pdf

R
FFF
AR
A A
a b a > 0b>a
a
b
∀ ∃
∀x≥0,∃n∈Nna ∈]x, x +b[.

R
[0,1] 0 ]0,1]
]0,1] x∈]0,1]
]0,1] x/2
0
A⊂R+A6=∅ ∅
A
Ainf A
(∀x∈A, x ≥inf A,
∀y > inf A, ∃x∈A, x < y.
inf ]0,1] = 0 inf Q∗
+= 0
AR
A m
∀x∈A, m ≤x.
Ainf A
A
G⊂RG
0∈G,
∀x∈G, −x∈G,
∀x∈G, ∀y∈G, x +y∈G .
G x ∈G n ∈Z
n.x ∈G
r
rZ:= {nr ;n∈Z}={0, r, −r, 2r, −2r, 3r, −3r, ..., nr, −nr, ...}
BY:
$
\
C

R
R
{0},N,Z,Q,[0,1],]−1,1[,R,3Z.
G∩]0,+∞[= {x∈G;x > 0}
r≥0rZ
GR
•G=rZr≥0
•R
R
G
G6={0}r
G∩]0,+∞[
r= inf G∩]0,+∞[= inf{x∈G;x > 0}.
r > 0x∈G x > r x ≥2r
r∈G G =rZ
r= 0
∀ > 0,∀x≥0,∃g∈G g ∈]x, x +[.
GR
α∈R\Q
Z[α] = {n+mα :n∈Z, m ∈Z}R
{ei2παm;m∈Z}
{z∈C;|z|= 1}
{z∈C;|z|= 1}
R
R
R
BY:
$
\
C

R
R
Rx+y
y+x
BY:
$
\
C

R
x−x
x y x +y
inf G∩]0,+∞[
0
Z[α] = {n+mα;n∈Z, m ∈Z}α∈Qα6∈ Q
Z[α]Z[α]
R
BY:
$
\
C