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Oct
21
comment General Linear Group of a vector space
Well, to be technical, you only need to pick a basis to determine the components of the matrix representing the isomorphism.
Oct
20
comment Maclaurin series for $e^z /\cos z$.
Perhaps some words or explanations would help this jumble of equations make sense...
Oct
20
comment Converging or diverging series?
One quick trick for (a) is to note if $a_{n}=\sqrt{n}\cos^{2}(n)/(n^{2}-2)$, then $0\leq a_{n}\leq \sqrt{n}/(n^{2}-2)$, since $0\leq\cos^{2}(n)\leq1$.
Sep
28
comment Question on category theory
Well, you describe a "locally-small" category, where the $\hom(-,-)$ are sets. They can be "bigger" collections (classes), which would give us a "large" category (example of a large cat: Set). THEN the question is: are you talking about the category of small categories, or of large categories? (Or both?)
Aug
14
comment Summing the series $ \sum_{n=1}^{\infty} \int_0^{\infty} \frac{\mathrm dx}{n(1+x^3)^n}$
@Norbert, you are too clever for my feeble old mind! ;) Thanks for the explanation, I appreciate it greatly.
Aug
13
comment Summing the series $ \sum_{n=1}^{\infty} \int_0^{\infty} \frac{\mathrm dx}{n(1+x^3)^n}$
I'm old and forgetful, so I have a question: when you use your clever trick $\log(1+q)=\sum\dots$, setting $q=(1+x^{3})^{-1}$, don't you need to be careful with the limits of integration and take $\int^{\infty}_{\epsilon}\dots\,\mathrm{d}x$, then take the limit as $\epsilon\to0^{+}$? [I know this may be pedantic, but as I said -- I am old and forgetful, and I forgot whether you can skip it or if it's really necessary!]
Aug
9
comment Understanding mathematical set theory syntax
@user2666425: the one-to-one correspondence is between the powerset of $A$ and $2^{A}$. There is not necessarily a one-to-one correspondence between the cardinality of $A$ with $2$! There is equal cardinalities between $P(A)$ -- the powerset of $A$ -- and $2^{A}$, the set of characteristic functions for all subsets of $A$.
Aug
9
revised Understanding mathematical set theory syntax
added 461 characters in body
Aug
9
answered Understanding mathematical set theory syntax
Aug
9
revised Understanding mathematical set theory syntax
Improved TeX
Aug
9
suggested approved edit on Understanding mathematical set theory syntax
Aug
6
revised Cohomology ring of $U(n)$
Improved TeX
Aug
6
suggested approved edit on Cohomology ring of $U(n)$
Aug
6
comment Closed form for this continued fraction
Rigorously speaking, $f(x)$ doesn't converge when $x\leq0$. If I recall correctly, this is by Worpitzky's theorem...I would be rather excited if I am wrong, though, and certainly do not rule it out!
Aug
5
comment Closed form for this continued fraction
I think he means "closed-form expression" the continued fraction...I'm guessing/hoping-since-I-already-answered ;p...
Aug
5
answered Closed form for this continued fraction
Aug
4
comment Name for this Sum
Well, it's not Euler's constant -_-' ...I think this question is too general, since we don't know anything specific about the $a_{n}$ coefficients or the sequence of products $b_{n}=\prod^{n}_{k=0}a_{k}$...
Aug
3
revised Optimize database indexes, the sequel
Improved grammar
Aug
3
suggested approved edit on Optimize database indexes, the sequel
Aug
3
revised Optimize database indexes, the sequel
Improved formatting