I have been working with Ross' Elementary Analysis and almost all examples of uniform convergence are either sequences of functions which converge to the zero function or are power series. I believe that I understand these rather simple, dry examples fairly well, but that I am left with an uninspired conception of uniform convergence. I was wondering if there were any other common, useful examples of uniform convergence in a case where the limit function isn't identically zero and the sequence of functions are not partial sums of a power series. I would like to see some more strange/surprising scenarios.
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1Power series are so not "dry and simple"! – hmakholm left over Monica Nov 22 '15 at 20:02
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1... but here is a construction that uses uniform convergence of something that isn't a power series. – hmakholm left over Monica Nov 22 '15 at 20:04