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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
Aug
3
suggested approved edit on Optimize database indexes, the sequel
Aug
3
comment Learning math: still paper and pen
When you write with a pen/pencil on paper, your brain is actually registering the words --- whereas typing registers the letters. Consequently, the overall notes written by hand (in any subject) "sticks" with you longer and better than those just typed up. Ideally, you'd write by hand on paper first, then type them up in LaTeX taking into account corrections, citations, more interesting examples, etc. etc. etc.
Aug
2
comment How to solve $f\frac{\partial^2f}{\partial x\partial y} = \frac{\partial f}{\partial x}\frac{\partial f}{\partial y}$
Perhaps if you change coordinates to $z=x+\mathrm{i}y$ and $\bar{z}=x-\mathrm{i}y$, you get something along the lines of Laplace's equation. That should be a good first step...