fn is a sequence of uniformly continuous real-valued functions on R. and fn converges pointwise to f. which is continuous but not uniformly continuous.
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f:[0, infty) ----> R is continuous. f(x) tends to a finite limit as x-->infty must f be uniformly continuous on [0,infty)? any counterexample
Originally Posted by szpengchao f:[0, infty) ----> R is continuous. f(x) tends to a finite limit as x-->infty must f be uniformly continuous on [0,infty)? We can assume that In this case, . Now I ask you is uniformly continuous on ? (Why or Why Not?) So what is your answer?
no, i think. for that function to be uni. continuous on [a,b], we need: and f(y) takes value L at and therefore we cannot have an arbitary small distance between x,y. i appreciate your way of "teaching."
If a function is continuous on a compact set, such as [0,N], is it uniformly continuous on that set?
yes
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