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I fill in "About Me" sections from time to time.


1d
answered $\sum a_n$ converges, $a_n \in \mathbb{R}$, then there exists real sequence $b_n$ such that $b_n\rightarrow +\infty$ and $\sum a_n b_n$ converges.
2d
revised Prove: $x^n=0 \to x=0$
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2d
comment Prove: $x^n=0 \to x=0$
You should appeal to an axiom in each of the "therefore" statements you make, or otherwise use a different approach.
2d
revised Prove: $x^n=0 \to x=0$
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2d
answered Prove: $x^n=0 \to x=0$
Jul
21
comment Prove $n^4 \equiv 1 \pmod{5}$
There's nothing wrong with wikipedia. The math articles are almost always useful. And if they are wrong, well isn't mathematics the queen of sciences because anyone can verify an argument?
Jul
19
comment $L^p$ integral on every measurable subset of $\Bbb R$
If the measure of $A$ is $\infty$, $||f||_1 \leq \infty$.
Jul
19
comment $L^p$ integral on every measurable subset of $\Bbb R$
More of hint: $\alpha=1/q$, $c=||f||_p$.
Jul
19
comment Find $\delta >0$ such that $\int_E |f| d\mu < \infty$ whenever $\mu(E)<\delta$
@phenomenalwoman4, you are welcome to accept this answer, but please do not the hole in the argument pointed out in the comments. The invalid step I made can be justified (or tweaked) easily for $X=R^n$, but you need to do more work otherwise.
Jul
19
comment Suggestion for Computing an Integral
There are two competing factors here. One is to get the bounds nice, the other to get the integrand nice. For the just the first octant portion, picking $x=2^{1/2}\rho \sin \phi \cos \theta$, $y=2 (\rho \sin \phi \sin \theta)^{1/2}$, and $z=6^{1/6}(\rho\cos \phi)^{1/3}$ gives the nice bounds $0\leq \rho \leq 1$, $0\leq \phi,\theta \leq \pi/2$, but the integrand is a mess. I haven't computed the Jacocian either.
Jul
19
comment Suggestion for Computing an Integral
@TylerHG, we search for $F$ such that $\nabla \cdot F = ...$, then use divergence to get a surface integral.
Jul
19
comment Suggestion for Computing an Integral
@semiclassical, that's an interesting idea, but I'm worried it will be hard to find a good vector field $F$ and the surface will still be bad
Jul
19
revised Prove $n^4 \equiv 1 \pmod{5}$
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Jul
19
comment Where can I find SOLUTIONS to real analysis problems?
WARNING: USE AT YOUR RISK. Don't copy for homework, the lack of knowledge you'll gain is your loss. Even if self studying, make sure to make a fair attempt at a solution.
Jul
19
revised Prove $n^4 \equiv 1 \pmod{5}$
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Jul
19
answered Prove $n^4 \equiv 1 \pmod{5}$
Jul
18
comment Engineer: Unable to appreciate importance of L2 space
I think a (the) reason is to do Fourier series, and to do fourier series, it makes sense to be in a Hilbert space, and $L^1$ is not a hilbert space but $L^2$ is special and has an inner product that makes it an hilbert spacec.
Jul
18
comment Prove $18080108080 \sum_{k=0}^{1560-1} 10^{10k}+1$ is prime
@Brad Something like: PrimeQ[Sum[10^(10*k), {k, 0, 1560 - 1}]*1808010808*10 + 1]; is better. Your code returns PrimeQ[1+10*null] .
Jul
18
revised Prove $18080108080 \sum_{k=0}^{1560-1} 10^{10k}+1$ is prime
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Jul
18
revised Prove $18080108080 \sum_{k=0}^{1560-1} 10^{10k}+1$ is prime
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