Basic Analysis I — Real Analysis · Problem 7.3.6

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · sequences-and-convergence

Problem

Let (X,d)(X, d) be a metric space where dd is the discrete metric. Suppose {xn}n=1∞\{x_n\}_{n=1}^\infty is a convergent sequence in XX. Show that there exists a K∈NK \in \mathbb{N} such that for all n≥Kn \geq K, we have xn=xKx_n = x_K.

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