(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let {x_n} be a sequence in a metric space such that the distance between x_i and x_{i+1} is epsilon for some fixed epsilon > 0 and for all i. Can it be shown that this sequence has no convergent subsequence?

2. Relevant equations

None.

3. The attempt at a solution

I'm afraid I have no clue on this one. I'm not 100 % sure that it's always true either, but it seems intuitive that it should be true. Any hints would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: This sequence has no convergent subsequence?

**Physics Forums | Science Articles, Homework Help, Discussion**