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Jun
14
comment Suppose $F$ is a field and the irreducible polynomial over $F$ of $x$ is of odd degree.
That's correct.
Jun
8
comment Imitating smaller Rubik's cubes with bigger ones.
I was talking about in the first paragraph
Jun
8
comment Imitating smaller Rubik's cubes with bigger ones.
I'm not reading your link since I'm on my phone, but you did skip mention of the step where you fix the positions that you might get on the "3-cube" that are impossible on a normal 3-cube.
Jun
6
answered Finite “snakes” in a connected space
Jun
6
comment What is the idea behind a projection operator? What does it do?
What's wrong with the current answers? Sure, the most popular one is a bit tongue in cheek (simply describing what idempotence means in a more colloquial setting), but the answers below it do describe projection mathematically in pretty clear detail.
Jun
5
comment Can any commutative ring of characteristic $p\in\mathbb P$ be written as the form $R/(p)$ with $R$ being a ring of characteristic $0$?
I highly doubt there's a universal lift to characteristic zero as you describe.
Jun
4
comment Presentation of the additive group of the rational numbers
You don't need the classification theorem to prove that $\mathbb Q$ is not finitely generated; it simply follows from the fact that every finitely generated subgroup of $\mathbb Q$ is cyclic, and $\mathbb Q$ is not a cyclic group.
Jun
4
comment Presentation of the additive group of the rational numbers
Or in additive notation, $\langle x_1, x_2, \ldots \mid n x_n = x_{n-1}, n \ge 2\rangle$.
Jun
3
comment What is the significance of stuff like the “Pigeonhole Principle”?
Good answer. ${}{}$
Jun
3
comment What is the significance of stuff like the “Pigeonhole Principle”?
Lmao. The article says definite evidence of alien life by 2025, ergo, worlds will meet very soon. Did you even read the article???
Jun
3
comment What is the significance of stuff like the “Pigeonhole Principle”?
What if you never wear a pair of socks of the same color?
Jun
2
comment Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)
Stefan might be saying this more rigorously (too lazy to figure it out), but: this solution is like assigning to $\mathbb R$ the topology obtained by identifying it with a subspace of $\mathbb R^2$ given by a circle and a tail. The fact that a 1-1 continuous path from $\mathbb R$ onto such a figure should be pretty intuitive, which is what makes the topology coarser.
May
29
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May
26
comment A question about Quadratic residue
I don't see how this helps. Let $q = 4np+2p-1$ be prime, then there exists an $a$ so that $-1 \equiv a^2 \mod q$, which means $a^2+1 = x(4np+2p-1)$ for some $x \in \mathbb Z$. Then $a^2+1 \equiv -x \mod p$, so... ??? Was this what you were suggesting, or did you have something else in mind?
May
26
revised A question about Quadratic residue
edited body
May
26
answered A question about Quadratic residue
May
25
comment Can I approximate a measurable set with an open set for integration purposes?
$X$ may not have an open subset; do you want to allow $f$ to be extended to a larger domain? If so, and $X$ is measurable then the answer to your question taken literally is yes, because you can extend $f$ to $\mathbb R$ so that $\int_{\mathbb R} f > \int_X f$, and then use intermediate value theorem on the family of open intervals $(-a, a)$ for $a \in \mathbb R^{\ge 0}$ (if $\mathbb R-X$ has measure zero, just take $X^O=\mathbb R$). But morally, I'm thinking it's likely what you want is more like an open set $X^O$ that differs from $X$ on a set of measure zero, in which case the answer is no.
May
22
reviewed Approve Proving an entire function is constant
May
22
comment Proving an entire function is constant
Per @DanielFischer's comment, assume the equation $\frac{(f(z))^3}{z^2} + f(z)=0$ is satisfied for all nonzero values of $z$, and see what $f$ can be.
May
22
revised Proving an entire function is constant
added 2 characters in body