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9h
answered Sequences formed by integer evaluations of polynomials modulo $ p^{k} $, where $ p $ is a prime number and $ k \in \Bbb{N} $.
12h
revised Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
added 339 characters in body
12h
comment Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
I'm waiting for the first one to complain that this "intuitively clear" argument is in fact Galois theory in disguise
12h
comment Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
@Gus The fact that these lengths occur in geometric constructions does not show that they are irrational (or incommensurable). In fact, claiming this might have gotttn you expelled from the academy back then ;)
12h
answered Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
12h
comment Elementary question in Group Theory with less prerequisite
The action of $G$ on its order-3 subgroups gives us a subgroup of $S_7$ where all nontrivilal elements look like $(1\,2\,3)(4\,5\,6)$ (two fixpoints would mean that $G$ has a subgroup of order $9\nmid 15$). "Of course" the product of permutations of this cycle type is not again of this type, but I don't see how to show that without gazillins of case distinctoins.
13h
revised Confusion between an element and its preimage
edited body
13h
comment Prove $\vdash\forall x(\alpha\to\beta)\to(\exists x\alpha\to\exists x\beta)$
Can you do $\forall x\beta\vdash \beta$ and $\beta\vdash\exists x\beta$?
18h
answered Is it possible that $1\otimes 1 = 0$?
18h
comment How to prove that $a^{|G|}=e$ if a $\in G $
This is essetnially just re-proving Lagrange in one line, but: the orbits under the action of $\langle a\rangle$ on $G$ by left multiplication are all of the same length, so ...
18h
comment how to embed a square into $R^2$?
Let $Q=\{\,(x,y)\in\mathbb R^2:\max\{|x|,|y|\}=1\,\}$. Then consider $Q\to\mathbb R^2$, $(x,y)\mapsto (\frac x{\sqrt{x^2+y^2}},\frac y{\sqrt{x^2+y^2}})$? - Actually, by inducing the unit circle's smooth structure, you reduce the problem to embedding $S^1$, don't you?
1d
awarded  Nice Answer
1d
answered What is the significance of using “$a$” vs “$x$” in this text?
1d
answered Group presentation of Integers $\big(\mathbb{Z,+}\big)$
1d
answered Can a unit of infinite order in algebraic integers of a number field be an arbitrarily high power of another unit?
1d
answered The Change-making problem algorithm proof (at the dynamic programming method)
1d
comment “Standard first term” of a series
The fist index is usually the firs element of $\mathbb N$ :)
1d
comment If $n$ is a natural number and $n$ is a $4th$ power and a $5th$ power prove it is a $20th$ power.
Consider the prime factorization of $n$
1d
comment Does this math formula with $1/PI\begin{cases}^\infty_{-\infty}\end{cases}$ mean anything?
So the best suggestion is to replace $\{$ with $\int$ and $PI$ with $\pi$.
1d
comment Homomorphisms between abelian groups
The asumption that $H,K$ be abealian is not needed