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1h
comment Why a Collection of disjoint open sets in $\mathbb R^n$ has only countably many nonempty sets?
@canseeker The $\Bbb Q^n$ argument is the way to go. There are only countably many rational points and every non-empty open set of a collection of disjoint open sets has such a point "of its own". Hence there can only be countably non-empty such sets.
8h
comment Soft Question: Why does the Axiom of Choice lead to the weirdest constructions?
Well, it doesn't really lead to constructions.
20h
comment Definable over $(\mathbb{R}, <, +, \cdot, 0, 1)$
Regarding c, the $k$-largest root of a fixed polynomial (of fixed degree) is definable. The
1d
answered $ \lim_{x\rightarrow a} f(x)= \lim_{x\rightarrow a} [f(x)]$ then at $x=a$ is there a maxima or minima?
1d
answered $f(x)=\sum_{k=0}^\infty c_kx^k$ converges for $|x|<R$ with $R>0$, $\exists x_n\ne0$ s.t. $x_n\to0$, $f(x_n)=0$ $\forall n$, then $c_k=0$ $\forall k$.
1d
comment What is an axiom in layman's terms?
@IttayWeiss Guntram's guess is right. I can never remember to adjust the spelling of Εὐκλείδης to English habits. Sorry for the .. inkonvenience
1d
awarded  Nice Answer
1d
answered What is an axiom in layman's terms?
1d
revised Why is $R((X))$ defined as follows?
added 507 characters in body
1d
revised Are 0 and -1 the only rational periodic solutions of $z_{n}\equiv z_{n-1}^{2}+c$?
added 10 characters in body
1d
answered Are 0 and -1 the only rational periodic solutions of $z_{n}\equiv z_{n-1}^{2}+c$?
1d
comment Are 0 and -1 the only rational periodic solutions of $z_{n}\equiv z_{n-1}^{2}+c$?
Do you want periodic or eventually periodic?
1d
comment How can i prove a closed ball is the closure of a open ball?
The statement is not true in general metric spaces, so you may want to mention your spaces of interest ...
1d
comment Constructing a 15+ vertex graph with specific conditions.
If the minimum degree equals 3, you cannot have an Eulerian circle, only an Eulerian path
1d
comment Constructing a 15+ vertex graph with specific conditions.
N.B. 2-connected means that the removal of 1 vertex does not disconnect the graph
1d
awarded  inequality
1d
comment How is the shape of a quadratic Bézier curve affected by the anchor points being equidistant or different distances from the control point?
As you speak of the control point, I assume you mean a quadratic Bézier curve. In that case the curve is a parabola tangent to the lines connecting anchor and control and relocating the control point (and/or the anchor points) causes an affine transformation of that parabola ...
1d
comment How to show $\frac{19}{7}<e$
@Bernard No. $\sum_{n=0}^3\frac1{n!}=\frac83<\sum_{n=0}^4\frac1{n!}=\frac{65}{24}<\frac{19}7$
1d
revised Why is $R((X))$ defined as follows?
added 253 characters in body
1d
comment Why is $R((X))$ defined as follows?
Hm, I assume the downvote is because I did not restate the formal definitions of all those constructs?