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May
23
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 ;)
May
23
answered Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
May
23
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.
May
23
revised Confusion between an element and its preimage
edited body
May
23
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 $\beta\vdash\exists x\beta$?
May
23
answered Is it possible that $1\otimes 1 = 0$?
May
23
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 ...
May
23
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?
May
23
awarded  Nice Answer
May
22
answered What is the significance of using “$a$” vs “$x$” in this text?
May
22
answered Group presentation of Integers $\big(\mathbb{Z,+}\big)$
May
22
answered Can a unit of infinite order in algebraic integers of a number field be an arbitrarily high power of another unit?
May
22
answered The Change-making problem algorithm proof (at the dynamic programming method)
May
22
comment “Standard first term” of a series
The fist index is usually the firs element of $\mathbb N$ :)
May
22
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 $n$
May
22
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 $\pi$.
May
22
comment Homomorphisms between abelian groups
The asumption that $H,K$ be abealian is not needed
May
22
comment Find Values of Riemman Zeta Function
Is there any value known to be omitted at all?
May
22
comment How to establish the distributive property of sum notation
You have a typo in your base case: $a_1+a_1$ should be $a_1+b_1$
May
22
answered How to establish the distributive property of sum notation