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8h
comment Hom(A, B) Cathegory theory
$\operatorname{Hom}(A,B)$ is the set of morphisms (in the category of interest) from object $A$ to object $B$. Often this set carries additional structure, for example in the category of vector spaces over a field $k$, $\operatorname{Hom}(A,B)$ is itself a vector space (per pointwise addition/multiplication). It is not clear which category you are working in, otherwise more could be said for the specific case
17h
answered Show that if $f$ is analytic on a domain $D$, and if $|f|$ is constant, then $f$ is constant.
18h
comment Is embedding a function make sense?
Definition 1.2 of the linked paper defines embedding for the purpose of the paper. The concept is loosely related to but not immediately recognizable as embedding in the sense of substructure within structure
21h
revised How to calculate $\frac1n$ sequence?
added 19 characters in body; edited title
21h
answered How to calculate $\frac1n$ sequence?
22h
comment Basic set theory
"not standard" is quite mild :)
22h
comment Question about “subset of topological space”
You $X$ is not a topology because the three properties of open sets do not hold. Also, a topology is not the same as a topological space (which is usually understood as the tuple consisting of the underlying set and the topology, and referred to by the underlying set alone if no confusion can arise)
23h
answered What does it REALLY mean for a metric space to be compact?
23h
comment What does it REALLY mean for a metric space to be compact?
"Compact is as close to finite as you can get"
23h
answered $\mathbb{Z}_6/\mathbb{Z}_2$ isomorphic to $\mathbb{Z}_3$?
1d
answered Guaranteed Profit on a Roulette wheel: Does $N$ exist?
1d
comment Question about “subset of topological space”
A subset of a topological space id formally merely a subset of the underlying set of the topological space. I think your notation $X=\{S,\emptyset,[4,3),(5,7](6,8]\}$ is confusing. Either you did not specify what the topology of $X$ is and merely listed the underlying set of the five points of $X$ (where the points look somewhat funny). Or you meant t have $S$ as underlying set of your space $X$ and $\{S,\emptyset,[4,3),(5,7](6,8]\}$ as its topology (i.e., set of open sets); but then this fails to be a topology as it does not contain $(5,7]\cap (6,8]=(5,6], for example.
1d
revised Determining the intersection of kernel and image.
added 24 characters in body
1d
answered Determining the intersection of kernel and image.
1d
revised Checkerboard with one gap can be covered by triominos?
edited title
1d
comment When is $\sum_{n=0}^{\infty}\frac{n^k}{3^n}$ an integer?
I took the liberty to submit the sequence to OEIS as A261811. I suggest you add your findings (and "stake your claim") once it has been approved.
1d
answered “Either A and B is open, then A + B is open” (typo sense-making, Stein Shakarchi Real Analysis)
2d
comment If the decimal expansion of $a/b$ contains “$7143$” then $b>1250$
You might have gone through older editions of Bundeswettbewerb Mathematik. In the year 1983 (I think), there was the exact same problem statement with "1983". Actually, it might have been any year between 1980 and 1999 because I remember that $\frac{19}{96}<\frac ab<\frac15$ could be used to show that $b>100$.
2d
answered If the decimal expansion of $a/b$ contains “$7143$” then $b>1250$
2d
comment How is $\mathbb N$ actually defined?
Don't you mean the first countable infinite ordinal?