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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple proof of uniform continuity

Loading...

Similar Threads for Simple proof uniform |
---|

I Convergence of ##\{\mathrm{sinc}^n(x)\}_{n\in\mathbb{N}}## |

B Proof of a limit rule |

B Proof of quotient rule using Leibniz differentials |

B Don't follow one small step in proof |

**Physics Forums - The Fusion of Science and Community**