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Dec
19
comment Handbook of mathematical drawing?
Honestly, learning how to draw in general helped me with technical diagrams and mathematical figures. Perhaps it's the only way...
Nov
23
comment How to find this limit: $A=\lim_{n\to \infty}\sqrt{1+\sqrt{\frac{1}{2}+\sqrt{\frac{1}{3}+\cdots+\sqrt{\frac{1}{n}}}}}$
I'm interested: how did you derive your approximation? (I ask because I wouldn't have a clue where to begin with deriving it...)
Nov
6
comment Derive the equation of motion from Lagrangian of a particle moving in an electromagnetic field
Uh, perhaps plug the Lagrangian into the Euler-Lagrange equations...?
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 $b_{n}=\prod^{n}_{k=0}a_{k}$...