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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
Aug
19
asked Finding $F(x)$ so that $F'(x) = e^{-x^2}$
Aug
19
revised If $\exp(itH) A \exp(-itH) = A$ for all $t$, do $A$ and $H$ commute?
Finicky. Just put the title into LaTeX and put "for all t" into "for all $t$"
Aug
19
suggested approved edit on If $\exp(itH) A \exp(-itH) = A$ for all $t$, do $A$ and $H$ commute?
Aug
19
awarded  Critic
Aug
19
accepted $|P(x)|$ differentiable at a root $x_0$