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comment Is this group given presentation isomorphic to $\mathbb{Z}_2$, and why?
Samarkand, I think it would be much better if you would ask the second question (about random group presentations) in a separate post, since it's an entirely different question. This would also give you an opportunity to sharpen the question: think about which probability measure would be the most meaningful to you and why, rather than leave the choice to the reader. (Just a suggestion.) I agree with YCor that the first question is substantial enough to stand on its own, and that it should not be migrated.
2d
comment Is this group given presentation isomorphic to $\mathbb{Z}_2$, and why?
It's probably not a good idea to alter the question after receiving an answer, in a way that makes the answer no longer relevant. I'm going to revert the tltle and change the body slightly so that Francesco's answer is still relevant.
Mar
30
comment Is this proof of the twin prime conjecture?
I agree with @Stella, and I'm a little surprised that there isn't more push-back against this type of post. Consider what happened in the case of math.sci, where the board became virtually overrun by posts about crankish solutions to famous open problems (e.g., James Harris). I would think users here would be way more circumspect and skeptical about posts about proposed solutions to notorious problems.
Mar
20
comment Why does this sequence converge to φ?
The only thing left to explain is why the sequence converges. But this isn't hard: it's an increasing sequence by an inductive argument, using the fact that $f(x) = \sqrt{1 + x}$ is monotone increasing (has positive first derivative). Also, an upper bound of the sequence exists ($2$ is an upper bound, again by an inductive argument which uses monotonicity). Thus the least upper bound of the sequence is the limit.
Mar
17
reviewed Approve Tensor product and Direct product.
Mar
10
answered Cantor's Theorem with Posets
Mar
9
comment Cantor's Theorem with Posets
You can often construct a bijection between the underlying sets: take $P$ to be the ordinal $\omega$. Since the poset $[P, 2]$ of poset maps $P \to \{0 \leq 1\}$ is identified with the poset of upward-closed subsets of $P$ (ordered by inclusion), there is an isomorphism $[P, 2] \cong \{\bot\} \sqcup P^{op}$ where we adjoin a bottom element $\bot$ to $P^{op}$. So both $P$ and $[P, 2]$ have countable cardinality.
Mar
9
comment Cantor's Theorem with Posets
Nit pick: the numeration looks a little off in the second paragraph. Since $b_0$ and $t_0$ are the bottom and top elements, we have $\phi(b_0) = \mathbf{0}$ and $\phi(t_0) =\mathbf{1}$; I think what you want at the end of the second paragraph is $b_1 = \phi^{-1}(f_0)$ and $t_1 =\phi^{-1}(g_0)$, or in other words $\phi(b_1) = f_0$ and $\phi(t_1) = g_0$.
Feb
28
comment Is there a more rigorous way to show these two sums are exactly equal?
Take your time; glad to help.
Feb
28
answered Is there a more rigorous way to show these two sums are exactly equal?
Feb
6
comment geodesic computation: “energy” minimization versus arc length minimization
Migrating to Math.SE on recommendation from several users...
Jan
30
revised Under what conditions the quotient space of a manifold is a manifold?
added another note
Jan
30
revised Under what conditions the quotient space of a manifold is a manifold?
added a reference
Jan
21
comment $\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
I'm guessing the downvote was in view of the obvious question: how do we know that fact about the normal distribution? Well, often it's proved starting from the fact that the OP is asking about, in effect running the very elementary calculus manipulations in your answer in reverse order. Meanwhile, there are various ways we know this fact, as mentioned by the OP, but he's asking specifically for a reason based on contour integration. So it seems you are not answering the question that was asked.
Jan
4
comment What is a number?
@vonbrand Yes, it's the one mentioned by Daniel Fischer. My own edition is in English.
Jan
2
comment dropping injectivity from multivariable change of variables
Also cross-posted at MO: mathoverflow.net/questions/227406/…
Dec
30
comment Limit problem with cosh and sinh
It's a fun problem, but off-topic for this site, which is for professional mathematicians and their graduate students to ask questions related to their research.
Dec
14
comment A structural view to the power set axiom: Is this axiom really justifiable?
Yes, so: my point is that you are addressing a question different from the one asked. OP wasn't asking about structures on the power set, but rather on the set of substructures.
Dec
14
comment A structural view to the power set axiom: Is this axiom really justifiable?
But $P(A)$, which I understand to be the power set of $A$, is not the set of substructures.