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5h
comment Has anyone ever explored $(\sin{x})^x$ , $(\cos{x})^x$, etc?
Even defining your integrand is problematic whenever $\cos x < 0$. And even if you restrict yourself to intervals where this doesn't happen, you'll get singularities at the endpoints when $x$ is negative...
7h
revised Is there anything wrong with this proposed proof of the irrationality of Euler's constant?
texifying, cleaning up some typos
10h
reviewed Reopen Recurrence relation for ternary sequence
1d
comment Why is the solution of an ordinary differential equation required to be defined on an interval?
I'll probably write an actual answer later when I have time unless someone else does, but the short version is: you want the solution's domain of definition to be connected, because if it isn't then the "differentialness" of the equation isn't very meaningful.
2d
reviewed Reopen As of August 2015, is the “set” of all gold medalists in the 2016 Olympics a set?
2d
reviewed Reopen What is meant by “functional analysis is the study of vector spaces endowed with a topology”
2d
reviewed Close $\int \left(\cos\left(e^{\sin(x)}\right)\right) \text{d}x$
2d
comment How to find $ab+cd$ given that $a^2+b^2=c^2+d^2=1$ and $ac+bd=0$?
Or you could not assume $a$ and $b$ are real, forget about the bounds, and get exactly the same proof except that $\alpha$ and $\beta$ are now also allowed to be complex...
2d
reviewed Edit and Reopen Polynomial equations of degree larger than 4
2d
revised Polynomial equations of degree larger than 4
deleted 3 characters in body
2d
comment Does the “alternating” harmonic series where only prime terms are negative converge?
If you want to quantify exactly how far away you got carried, you could read up on Mertens' second theorem...
Aug
24
reviewed Close Senate elections statistics problem
Aug
23
comment Find all $n\times n$ matrices $A$ satisfying $\det(I+A^n)=(1+\det(A))^n$
To generalize both of the previous comments, $A$ could be any matrix whose eigenvalues are all equal — if $k$ is the only eigenvalue of $A$, then both sides are equal to $(1+k^n)^n$. If $n=2$, it's not hard to show that these are the only possible $A$; for larger $n$, they seem not to be...
Aug
23
reviewed Reopen What is the probability that this harmonic series with randomly chosen signs will converge?
Aug
23
revised Logarithm question, does $\ln \sqrt{7}$ equal to zero?
formatting, etc
Aug
23
revised Logarithm question, does $\ln \sqrt{7}$ equal to zero?
formatting, etc
Aug
23
comment Fields medalists who didn't study mathematics in college or university
In addition to being the only physicist ever to win a Fields medal, Ed Witten is likely the only Fields medalist whose bachelors degree is in history. (Though he does have a Ph.D. in physics.)
Aug
23
comment Fermat's last theorem concise proof - is it correct?
Either the proof is concise enough to reproduce in full here — in which case it should be reproduced in full here — or it isn't — in which case this question is too broad.
Aug
22
comment What should the initial guess be for the Bablyonian method of calculating square roots?
This is hard to answer unless you precisely specify your criterion for "better". A reasonable candidate would be the floor (or ceiling) of your square root (since those are the best possible integer guesses).
Aug
20
reviewed Edit Show that $\displaystyle{\int_{0}^{\infty}\!\frac{x^{a}}{x(x+1)}~\mathrm{d}x=\frac{\pi}{\sin(\pi a)}}$