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seen Dec 11 '13 at 22:38

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Aug
21
revised What do finite, infinite, countable, not countable, countably infinite mean?
Changed Z, Q, C
Aug
21
suggested suggested 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
Aug
19
revised Finding $F(x)$ so that $F'(x) = e^{-x^2}$
added 158 characters in body
Aug
19
comment Finding $F(x)$ so that $F'(x) = e^{-x^2}$
I see. Examining the graph of $\exp(-x^2)$ I see that $f'(0)$ is indeed $0$ but did you surmise this a different way?
Aug
19
comment Finding $F(x)$ so that $F'(x) = e^{-x^2}$
Yes you are right. Thank you