My Math Forum Uniform continuity of a function

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 January 19th, 2019, 03:06 PM #1 Newbie   Joined: Jan 2019 From: Poland Posts: 1 Thanks: 0 Uniform continuity of a function How to prove that f(x)=sin(1/x) isn't uniformly continuous in (0,1)? Last edited by skipjack; January 19th, 2019 at 06:10 PM.
 January 19th, 2019, 05:53 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,769 Thanks: 626 Math Focus: Yet to find out. Starting with the definition could be useful. Thanks from topsquark Last edited by skipjack; January 20th, 2019 at 01:16 AM.
 January 19th, 2019, 06:18 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,618 Thanks: 2608 Math Focus: Mainly analysis and algebra The peaks and troughs of $\sin \frac1x$ get infinitely close as $x$ gets close to zero. What does this mean when $\epsilon < 2$? Thanks from topsquark Last edited by skipjack; January 20th, 2019 at 01:14 AM.

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