If the function(adsbygoogle = window.adsbygoogle || []).push({}); f:→ℝ is uniformly continuous and a is any number, show that the function a*Df:→ℝ also is uniformly continuous.D

Ok, so I am just learning my proofs so be patient with me, i'm very new at it.

take a>0, ε>0 and x,y in D. We know |x-y|<δ whenever |f(x)-f(y)|<ε.

If we take a*f:→ℝ, we have |a*f(x)-a*f(y)|<ε → |a*[f(x)-f(y)]|<ε→D

a*|f(x)-f(y)|<ε→ |f(x)-f(y)|<ε/a. Therefore, if we use ε/a, the result is proven.

This just seems a little too easy to me, plus I've only done a few of these on my own. any suggestions/advice are greatly appreciated. Also, do I need to do this separately for a<0?

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# Simple proof of uniform continuity

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