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

Why is it that continuous functions do not necessarily preserve cauchy sequences.

2. Relevant equations

Epsilon delta definition of continuity

Sequential Characterisation of continuity

3. The attempt at a solution

I can't see why the proof that uniformly continuous functions preserve cauchy sequences doesn't hold for 'normal' continuous functions.

In particular the example of f(x) = 1/x on (0,1)

I have worked through the examples

http://www.mathcs.org/analysis/reals/cont/answers/fcont3.html

and here

http://www.mathcs.org/analysis/reals/cont/answers/contuni4.html

where they address this issue directly, but I can't get my head around it.

I understand that if we have a cauchy sequence converging to 0, then f(x_{n}) is going to diverge to infinity, but I still can't see what the problem is.

Any explanation you can offer would be appreciated.

Kind regards

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# Homework Help: Intuitive Explanation For Why Continuous functions do not preserve Cauchy sequences

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