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Miklós Schweitzer
2020 Miklós Schweitzer
2
2
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2020 Miklós Schweitzer
Problems
(1)
periodic continuous implies sequence is dense
Source: Miklos Schweitzer 2020, Problem 2
12/1/2020
Prove that if
f
:
R
→
R
f\colon \mathbb{R} \to \mathbb{R}
f
:
R
→
R
is a continuous periodic function and
α
∈
R
\alpha \in \mathbb{R}
α
∈
R
is irrational, then the sequence
{
n
α
+
f
(
n
α
)
}
n
=
1
∞
\{n\alpha+f(n\alpha)\}_{n=1}^{\infty}
{
n
α
+
f
(
n
α
)
}
n
=
1
∞
modulo 1 is dense in
[
0
,
1
]
[0,1]
[
0
,
1
]
.
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