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9m
comment Is the intersection of a finite language and an infinite language always a regular language?
The intersection of finite and infinite is certainly finite, hence regular
12m
comment Is there any relation Trace and Boundary?
Not really, I suppose. We may interprete "trace" as meaning something like "footprint", in the the linked pdf th e"footprint" the function leaves on the boundary, and for matrices just meaning as much as "a characteristic property"
4h
comment Identification of a quadrilateral as a trapezoid, rectangle, or square
Question 75 before the OP question asks to name an angle and I wondered why $\langle DBC$ was not among the suggestions, which shows that there is not the angle frmed by the dashed rays ... Nevertheless, I would certainly fail Q71 :)
5h
comment Fields of arbitrary cardinality
Hm, but wouldn't multiplication be noncommutative here? I guess taking the polynomial ring with all elements of $X$ as variables, i.e. using maps $X\to\mathbb N_0$ with finite support in place of finite strings might be better.
5h
comment Fields of arbitrary cardinality
+1 for not being "choicy". - $f_0$ corresponds to the empty string, hence need not play a special role.
5h
answered If I know the order of every element in a group, do I know the group?
6h
revised Distances to the center of points uniformly distributed in a disk
added 74 characters in body
6h
answered Distances to the center of points uniformly distributed in a disk
10h
answered Non-empty intersection of specific sets
1d
answered Sequences formed by integer evaluations of polynomials modulo $ p^{k} $, where $ p $ is a prime number and $ k \in \Bbb{N} $.
1d
revised Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
added 339 characters in body
1d
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
1d
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 ;)
1d
answered Understanding why $a+b\sqrt {2}\neq \sqrt {3} $
1d
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.
1d
revised Confusion between an element and its preimage
edited body
1d
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 $\beta\vdash\exists x\beta$?
1d
answered Is it possible that $1\otimes 1 = 0$?
1d
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 ...
1d
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?