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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: 1,801 Thanks: 636 Math Focus: Yet to find out. 
Starting with the definition could be useful.
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: 7,657 Thanks: 2635 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 $\epsilon < 2$?
Last edited by skipjack; January 20th, 2019 at 01:14 AM. 

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continuity, function, uniform 
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