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Aug
26
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.
Aug
26
reviewed Reopen As of August 2015, is the “set” of all gold medalists in the 2016 Olympics a set?
Aug
26
reviewed Reopen What is meant by “functional analysis is the study of vector spaces endowed with a topology”
Aug
25
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...
Aug
25
reviewed Edit and Reopen Polynomial equations of degree larger than 4
Aug
25
revised Polynomial equations of degree larger than 4
deleted 3 characters in body
Aug
25
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
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
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 $\displaystyle{\int_{0}^{\infty}\!\frac{x^{a}}{x(x+1)}~\mathrm{d}x=\frac{\pi}{\sin(\pi a)}}$
Aug
20
revised Show that $\displaystyle{\int_{0}^{\infty}\!\frac{x^{a}}{x(x+1)}~\mathrm{d}x=\frac{\pi}{\sin(\pi a)}}$
titles should have some non-MathJax component, and should not use \displaystyle
Aug
20
comment Prove the function is periodic
@EugenCovaci: $\lceil a \rceil$ is the smallest integer which is at least $a$, so $\lceil a \rceil \geq a$ by definition. Perhaps you are confusing it with $\lfloor a \rfloor$?
Aug
20
revised Prove the function is periodic
deleted 10 characters in body
Aug
20
answered Prove the function is periodic
Aug
20
reviewed Leave Open Share the beer fairly in a finite number of pours
Aug
19
revised 2-form whose self-wedge does not vanish?
edited tags
Aug
19
answered 2-form whose self-wedge does not vanish?