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January 19th, 2019, 03:06 PM   #1
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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.
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January 19th, 2019, 05:53 PM   #2
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Starting with the definition could be useful.
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Last edited by skipjack; January 20th, 2019 at 01:16 AM.
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January 19th, 2019, 06:18 PM   #3
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The peaks and troughs of $\sin \frac1x$ get infinitely close as $x$ gets close to zero. What does this mean when $\epsilon < 2$?
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Last edited by skipjack; January 20th, 2019 at 01:14 AM.
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