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

Prove that if f is uniformly continuous on [a,b] and on [a,c] implies that f is uniformly continuous on [a,c].

2. Relevant equations

3. The attempt at a solution

This is my rough idea for a proof, can someone help be say this more formally? Is my thinking even correct?

Let epsilon > 0.

Then there is some delta_1 for [a,b] and some delta_2 for [b,c].

Then the minimum of delta_1 and delta_2 is the delta we want for [a,c].

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# Homework Help: Real Analysis Continuity

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