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## Homework Statement

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

## Homework Equations

Epsilon delta definition of continuity

Sequential Characterisation of continuity

## 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