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Lebl-Basic-Analysis-I
· Problem 7.3.5
Metric Spaces
Mathematics · sequences-and-convergence
Problem
Suppose
{
x
n
}
n
=
1
∞
\{x_n\}_{n=1}^\infty
{
x
n
}
n
=
1
∞
converges to
p
p
p
. Suppose
f
:
N
→
N
f \colon \mathbb{N} \to \mathbb{N}
f
:
N
→
N
is a one-to-one function. Show that
{
x
f
(
n
)
}
n
=
1
∞
\{x_{f(n)}\}_{n=1}^\infty
{
x
f
(
n
)
}
n
=
1
∞
converges to
p
p
p
.
Related theory
Sequences Convergence Cauchy Sequences Subsequences
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