uniform continuity theorem

Apr 2010
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1
The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?
 

Drexel28

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Nov 2009
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Berkeley, California
The uniform continuity theorem says if f: A->N is continuous and Kin A is compact, then f is uniformly continuous on K.

But if I take 1/n on [0,1] it is not uniformly continuous because as we approach 0 from the left the y values get further and further apart. Is tehre something I'm missing in this theorem?
This makes no sense whatsoever. What's your function? Are you saying that \(\displaystyle f\left(\frac{1}{n}\right)\) isn't Cauchy?
 

Defunkt

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Aug 2009
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Israel
f is not defined at 0, therefore not continuous there. That theorem requires (although you didn't state it) that f is continuous in K.
 
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