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Feb
27
comment Proving that if a sequence converges weakly, then their set of norms is bounded.
Uniform boundedness principle, a.k.a. Banach–Steinhaus?
Feb
26
comment Why is the ring of integers initial in Ring?
@MarianoSuárez-Alvarez Ah, that makes sense. Sorry I didn't catch on.
Feb
26
answered Why is the ring of integers initial in Ring?
Feb
26
comment Why is the ring of integers initial in Ring?
@MarianoSuárez-Alvarez Surely, any ring is a $\mathbb{Z}$-algebra, and the dot must be multiplication by a scalar in that algebra?
Feb
26
comment Series Convergence $\sum_{n=1}^{\infty} \frac{1}{n} \left(\frac{2n+2}{2n+4}\right)^n$
@LudovicoL Yes, since $(1-1/k)^{k-2}\to e^{-1}$ when $k\to\infty$, and the harmonic series diverges.
Feb
26
answered Series Convergence $\sum_{n=1}^{\infty} \frac{1}{n} \left(\frac{2n+2}{2n+4}\right)^n$
Feb
25
comment Mathematical induction for inequalities
That's it, indeed. The sum of the middle positive term and the one negative term is easily simplified, so start there. You can get fancy and use the AM-HM inequality, or you can get the needed inequality by hand.
Feb
25
comment Differential Geometry-Wedge product
There are many equivalent ways of organizing the definitions that go into that, and the answer to your question depends on which one of them has been used.
Feb
25
answered Mathematical induction for inequalities
Feb
25
comment Mathematical induction for inequalities
Please learn a bit of LaTeX and use it. And when you do write inline fractions like $1/(n+1)$, don't omit the parentheses. It will confuse your readers no end. I fixed it for you this time around.
Feb
25
revised Mathematical induction for inequalities
LaTeX
Feb
24
comment Prove $\lim_{n\to \infty}b_n=\infty$.
The sequence is not likely to be non-decreasing. Imagine a humongous $a_n$ followed by a bunch of tiny terms …
Feb
24
answered Prove $\lim_{n\to \infty}b_n=\infty$.
Feb
23
comment The definition of open set in metric space and general topological zpace
I don't understand the question. In a topological space, there is no definition of open set that I know of. Rather the open sets are given, and assumed to satisfy certain axioms (that are indeed satisfied by the open sets in metric space).
Feb
23
comment How is it possible to change the pitch and the tempo of an audio track independently of each other?
Not directly an error, perhaps, but the trouble with the Fourier transform is that it is global, whereas here you need to make frequency changes that are local in time. The solution to this quandary might involve windowed Fourier transforms, about which I know nothing but the name, or wavelet analysis. Or something else entirely – but the global nature of the Fourier transform is key to the difficulty.
Feb
23
comment How is it possible to change the pitch and the tempo of an audio track independently of each other?
That's a good question, though I don't know if it belongs here. I hope it won't get closed, however, since there may be some interesting mathematics lurking in an answer. (If I were to guess, I imagine something along the lines of doing a wavelet transform, then stretching either the time or the frequency scale, and doing an inverse transform. But what do I know?)
Feb
23
comment Root of real and complex polynomial
I think you have it exactly backward.
Feb
23
comment Root of real and complex polynomial
Did you try to take the complex conjugate of the whole equation $\sum a_kx^k=0$?
Feb
23
answered Can $n^4 + n^3 + n^2 + n + 1$ for $n \in \mathbb{N} \backslash \{ 0,3\}$ yield a perfect square number?
Feb
23
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