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Apr
21
comment 1 to the power of infinity, why is it indeterminate?
@Noein: Oops, thanks for pointing it out. In order to not gratuitously bump this to the front page, I will let it stand as is. Hopefully, people will read the comments if the mistake confuses them.
Apr
11
comment Angle Sum of Self-intersecting polygon
@JayLemmon I don't think I claimed that the summing to $\pm2\pi$ is sufficient for the polygon to be non-self-intersecting. It will be sufficient if all the turns have the same sign; then the polygon will be convex. But in general, counterexamples are quite easy to make, as you say.
Mar
29
comment How to prove that Pumping lemma can't be used to prove regular languages.
It seems you need an example of a non-regular language which satisfies the conclusion of the pumping lemma. Does that help?
Mar
23
comment Convergence of sequence of a function
You might try playing with the function $f(x)=\sin(1/x)$ for $x\ne0$, $f(0)=0$, and $c=0$.
Mar
21
answered logarithmic limit in R^n
Mar
10
awarded  Informed
Mar
9
comment Let $p_n$ be the $n$th prime, for any integer $n$, prove that: $p_n+p_{n+1}\geq{p_{n+2}}$
@DDaren \sim will come out as $\sim$.
Mar
9
comment Can $n^4 + n^3 + n^2 + n + 1$ for $n \in \mathbb{N} \backslash \{ 0,3\}$ yield a perfect square number?
@Silenttiffy Because we're looking for a perfect square, meaning the square of an integer, so $n^2+n/2+x$ has to be an integer. Given that $n$ is an integer, that means $2x$ must be an integer.
Mar
7
comment Can $n^4 + n^3 + n^2 + n + 1$ for $n \in \mathbb{N} \backslash \{ 0,3\}$ yield a perfect square number?
@Silenttiffy Try $x=0$: $(n^2+n/2)^2=n^4+n^3+n^2/4<n^4+n^3+n^2+n+1$. Or try $x=1$: $(n^2+n/2+1)^2=n^4+n^3+\frac94n^2+n+1>n^4+n^3+n^2+n+1$.
Mar
5
answered Deduce that if $A$ is a subset of $C$, then $\sup A\leq \sup C$.
Mar
5
comment Deduce that if $A$ is a subset of $C$, then $\sup A\leq \sup C$.
To your last question: Yes, that is possible. But it has no bearing on the main question.
Mar
4
comment Simplify the function of x
To me, this answer looks right if the question were about the limit of $(1+x)(1+x^2)(1+x^4)\cdots(1+x^{2^n})$. What am I missing?
Mar
4
comment Simplify the function of x
Convolution is something like this: $f*g(x)=\int_{-\infty}^\infty f(t)g(x-t)\,dt$.
Mar
4
comment Simplify the function of x
But please, don't use $*$ for multiplication. That is the symbol for convolution. (I fixed it for you.)
Mar
4
revised Simplify the function of x
Don't use * for multiplication
Mar
1
comment What does omega limit sets have with invariant sets?
That invariant sets only exists in two dimensions, is news to me. I think your perception that this is so is an artifact of your textbook, which (I guess) does all the theory in two dimensions first.
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?