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Uniform Continuity 
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#1
Oct3005, 02:28 PM

P: n/a

"Suppose f:[0, inf) > R is such that f is uniformly continuous on [a, inf) for some a>0. Prove that f is uniformly continuous on [0, inf)."
But this is not true, is it? Consider the function [tex]f(x)=\left\{\begin{array}{cc}x &\mbox{ if }x\geq 1\\ \frac{1}{x1} &\mbox{ if }x<1\end{array}\right[/tex] 


#2
Oct3005, 02:54 PM

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P: 16,098

Hah! The question forgot to state that f is supposed to be a continuous map [itex][0, +\infty) \rightarrow \mathbb{R}[/itex]!



#3
Oct3005, 02:58 PM

P: n/a

Phew! It's not just me then.



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