Basic Analysis I — Real Analysis · Problem 7.3.5

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · sequences-and-convergence

Problem

Suppose {xn}n=1∞\{x_n\}_{n=1}^\infty converges to pp. Suppose f:N→Nf : \mathbb{N} \to \mathbb{N} is a one-to-one function. Show that {xf(n)}n=1∞\{x_{f(n)}\}_{n=1}^\infty converges to pp.

Related theory

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