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location Seattle, WA
age 44
visits member for 4 years, 3 months
seen 1 hour ago

Software engineer and long-time dabbler in mathematics; 11th in the Putnams forever ago but I've long since atrophied.


23h
comment SEVEN - NINE= EIGHT
@goblin I suspect the downvotes (and close vote) are also because the question is given without any hint of effort on OP's part, and possibly because of suspicions (given the phrasing) that the puzzle is from a contest or assignment somewhere.
23h
revised Proof that $\sin 10^\circ$ is irrational
Added a paragraph on angle trisection
1d
answered What does multiplication of two quaternions give?
1d
awarded  Nice Answer
1d
revised Proof that $\sin 10^\circ$ is irrational
Minor notation fixes
1d
comment Proof that $\sin 10^\circ$ is irrational
@lhf I was in the process of writing up my answer with just that tool, in fact!
1d
answered Proof that $\sin 10^\circ$ is irrational
1d
comment Proof that $\sin 10^\circ$ is irrational
The cubic polynomial has three roots, and there's no clean explicit form for the real one - but just knowing that it's the solution of a cubic isn't enough to show that the root isn't rational.
1d
comment $|G|=p^2$ then $G \cong \mathbb Z_{p^2}$ or $G \cong \mathbb Z_{p} \times \mathbb Z_{p}$
(Incidentally, I've TeXified your post more, fixing brackets and such; I encourage having a look at artofproblemsolving.com/Wiki/index.php/LaTeX:Symbols as a resource for the various math symbols. You might want to consider using $e$ for your group identity instead of $1$ since the latter has an arithmetic meaning that's not generally consistent with being the identity, but that's a personal choice...)
1d
revised $|G|=p^2$ then $G \cong \mathbb Z_{p^2}$ or $G \cong \mathbb Z_{p} \times \mathbb Z_{p}$
TeX fixes
1d
comment $|G|=p^2$ then $G \cong \mathbb Z_{p^2}$ or $G \cong \mathbb Z_{p} \times \mathbb Z_{p}$
Your 'but then $\{1\}=G\backslash\langle x\rangle$' doesn't seem to immediately follow from the statements before it; you might want to flesh that out more.
1d
comment $f: \mathbb{R} \to \mathbb{R} $ by $f(x) =\frac 1{1+x^2}$ is uniformly continuous on $\mathbb{R} $
@dustin I suspect that is often the case, but don't want to presume the worst (and didn't want to accuse here).
1d
comment $f: \mathbb{R} \to \mathbb{R} $ by $f(x) =\frac 1{1+x^2}$ is uniformly continuous on $\mathbb{R} $
It is considered very bad form to destructively edit a question after receiving your answer.
1d
revised $f: \mathbb{R} \to \mathbb{R} $ by $f(x) =\frac 1{1+x^2}$ is uniformly continuous on $\mathbb{R} $
rolled back to a previous revision
2d
comment Help finding the residue of $1/(z^8+1)$
Your first factorization looks incorrect - e.g., it suggests that $i^{1/8}$ is a root of $z^8+1=0$ (i.e. $z^8=-1$) when clearly $(i^{1/8})^8=i$.
Nov
23
comment Limit of $\lim_{x\to\infty} (1+\frac{f(x)}{x})^x$ for $f(x) = o(x)$
You shouldn't need an image for this - all of this is writeable in MathJax.
Nov
22
comment Surprising identities / equations
I presume there's some relatively clean bijection based around a canonical cycle structure of a permutation that explains this?
Nov
20
comment How to find a general sum formula for the series: 5+55+555+5555+…?
Agreed - this is one of the finest 'simple' answers I've ever seen on this site.
Nov
20
comment Poisson Distribution finding $E(x^4)$
What have you tried, what are your thoughts on the problem? Your 'given' formula looks incorrect to me; where did you obtain it from?
Nov
19
comment What does “The closure of the shift-orbit of the Fibonacci word” mean?
This is a fine answer but I'm worried that it might be over OP's head yet. An example of a word that's in the closure but not in the shift-orbit proper would go a long way, but at least at first glance I can't see any reasonably explicit way of defining such a word (IIRC this is coupled pretty closely to some of Connes' noncommutative geometry and specifically the examples on Penrose tilings)