# Proof of Cauchy Criterion for Riemann Integrals

1. Apr 3, 2010

### S.N.

1. The problem statement, all variables and given/known data
Some proofs I've looked at vary, but they generally follow the format show here: http://en.wikibooks.org/wiki/Real_Analysis/Riemann_integration#Theorem_.28Cauchy_Criterion.29

This isn't a question about an exercise, but rather a request for a clarification or a way of putting part of the proof in more understandable terms. My issue is the <= direction of the proof. I don't understand much about it. We're picking a $$\delta$$, sure, but then I don't see where the 1/n comes from, or what the business with m<n is, or just about anything in the 'reverse direction' of this proof. Does anyone have maybe a link to a proof with more heuristics, or if you have the time and patience, maybe a more intuitive way of describing that's going on?

Thanks for any help.