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 Aug 23 answered Checking Uniform Convergence Aug 23 revised Checking Uniform Convergence added 331 characters in body Aug 23 asked Checking Uniform Convergence Aug 21 revised What do finite, infinite, countable, not countable, countably infinite mean? Changed Z, Q, C Aug 21 suggested approved edit on What do finite, infinite, countable, not countable, countably infinite mean? Aug 21 comment What do finite, infinite, countable, not countable, countably infinite mean? If you do not know what $\mathbb{ Z, Q, R, C}$ are, then you need to build up some baseline knowledge before proving there are "more" real numbers than integers. Qiaochu is right in that Wikipedia will serve you best for now. Aug 21 answered Real life applications of Topology Aug 21 answered Proving that a bounded, continuous function has a supremum Aug 21 accepted Proving that a bounded, continuous function has a supremum Aug 21 comment Proving that a bounded, continuous function has a supremum how does part (b) look now that it has been revised? Aug 21 revised Proving that a bounded, continuous function has a supremum deleted 159 characters in body Aug 21 comment Proving that a bounded, continuous function has a supremum Unfortunately, we have not used the fundamentals of open balls and coverings so that machinery is unavailable to me... Aug 21 revised Proving that a bounded, continuous function has a supremum added 942 characters in body Aug 21 comment Proving that a bounded, continuous function has a supremum We have not defined compactness, we are supposed to do these problems simply with continuity and Bolzano-Weierstrass Aug 21 comment Proving that a bounded, continuous function has a supremum I am unsure what you mean by "carefully define your $c_n$." I know that I cannot simply say "let $c_n$ be such that $U - 1/n \le f(c_n) \le U$" but I am unsure how else to go about constructing such a $c_n$. Aug 21 asked Proving that a bounded, continuous function has a supremum Aug 20 answered Popular math books with depth Aug 20 comment Popular math books with depth @Iyengar If you loved Fearless Symmetry, then you should read Symmetry and the Monster by Mark Ronan amazon.com/Symmetry-Monster-Greatest-Quests-Mathematics/dp/… Aug 19 accepted Finding $F(x)$ so that $F'(x) = e^{-x^2}$ Aug 19 comment Finding $F(x)$ so that $F'(x) = e^{-x^2}$ Good point @Micah