# Mike

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 Aug23 revised Why do we use the commutator bracket for Lie algebra's cleaned it up slightly Aug23 suggested approved edit on Why do we use the commutator bracket for Lie algebra's Aug23 comment Checking Uniform Convergence @Matt xkcd.com/105 Aug23 comment Checking Uniform Convergence But it will only let me accept my own answer in 2 days as I have just found out, so if someone posts an answer before then I'll accept it. Aug23 answered Checking Uniform Convergence Aug23 revised Checking Uniform Convergence added 331 characters in body Aug23 asked Checking Uniform Convergence Aug21 revised What do finite, infinite, countable, not countable, countably infinite mean? Changed Z, Q, C Aug21 suggested approved edit on What do finite, infinite, countable, not countable, countably infinite mean? Aug21 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. Aug21 answered Real life applications of Topology Aug21 answered Proving that a bounded, continuous function has a supremum Aug21 accepted Proving that a bounded, continuous function has a supremum Aug21 comment Proving that a bounded, continuous function has a supremum how does part (b) look now that it has been revised? Aug21 revised Proving that a bounded, continuous function has a supremum deleted 159 characters in body Aug21 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... Aug21 revised Proving that a bounded, continuous function has a supremum added 942 characters in body Aug21 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 Aug21 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 $c_n$. Aug21 asked Proving that a bounded, continuous function has a supremum