Reputation
Next tag badge:
997/1000 score
274/200 answers
Badges
10 157 301
Newest
 Yearling
Impact
~1.6m people reached

1h
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
5h
comment Basic set theory
"not standard" is quite mild :)
5h
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)
6h
comment What does it REALLY mean for a metric space to be compact?
"Compact is as close to finite as you can get"
7h
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
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
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 $b>100$.
1d
comment How is $\mathbb N$ actually defined?
Don't you mean the first countable infinite ordinal?
1d
comment How is $\mathbb N$ actually defined?
If $0$ occurs in your Peano axioms the $0\in\mathbb N$. If you replace $1$ for $0$ in them, then $0\notin \mathbb N$.
1d
comment Solving an equation $x^{22}\equiv2 \bmod 23$
@DietrichBurde not for all $x$.
1d
comment What does a left-continuous version of a function mean?
Could it be that $f^-(x):=\lim_{t\to x^-}f(t)$?
1d
comment Let $V=\bigcup_{i=1}^n W_i$ where $W_i$ s are subspaces of a vector space $V$. Show that $V=W_r$ for some $1 \leq r \leq n$.
@user118494 "Let $W_1\cup W_2$ is a subspace of a vector space $V$ iff $W_1\subseteq W_2$ or $W_2\subseteq W_1$." happens to be true alo over finite fields and at any rate cannot readily be extended to $n>2$. Henc $W_1\subseteq \ldots \subseteq W_n$ is not something we already know
2d
comment Let $V=\bigcup_{i=1}^n W_i$ where $W_i$ s are subspaces of a vector space $V$. Show that $V=W_r$ for some $1 \leq r \leq n$.
@JyrkiLahtonen That's a really elegant proof for the claim by the way
2d
comment Let $V=\bigcup_{i=1}^n W_i$ where $W_i$ s are subspaces of a vector space $V$. Show that $V=W_r$ for some $1 \leq r \leq n$.
Yes, now you mention that $F$ should be infinite. But where do you use it? More to the point, how do you justify the "from what you already know" (it can't be justified)
2d
comment Let $V=\bigcup_{i=1}^n W_i$ where $W_i$ s are subspaces of a vector space $V$. Show that $V=W_r$ for some $1 \leq r \leq n$.
Where do you use that the ground field is infinite? If you don't your proof must be wrong (because the result is wrong if $|F|\le n$)
2d
comment Is it legal to define a function like this?
If $x\in\mathbb C$, then this is not really a recursion, you are missing the base case(s)
2d
comment Let $V=\bigcup_{i=1}^n W_i$ where $W_i$ s are subspaces of a vector space $V$. Show that $V=W_r$ for some $1 \leq r \leq n$.
Well, the linked questions have answers with self-contained proofs for the infinite case. So what makes this question a non-duplicate?
2d
comment Probability that a natural number is a sum of two squares?
@user7530 That's exactly why they are independent. See, of the numbers $1,\ldots,210000$ exactly $70000$ are divisible by $3$, exactly $30000$ are divisible by $7$ and exactly $10000$ are divisible by both. Hence exactly $\frac17$ of those divisible by $3$ are additionally divisible by $7$, and of those $140000$ not divisible by $3$ exactly $\frac17$ ($20000$) are divisible by $7$. Hence divisibility by $7$ is completely independent of divisibility by $3$. Thus a share $(1-\frac13)(1-\frac17)$ of these $210000$ numbers is divisible by neither $3$ nor $7$.
2d
comment If $L(v_1)=L(v_2)=L(v_3)=w_1$ then what is the $rank(L)$?
a) yes. and b) $2$. But you should not restrict to $\in\mathbb Z$
2d
comment Representable numbers in binary system but not in decimal system
Note that $q\times 2^{-m}$ with $m>0$ and $q\in\mathbb Z$ equals $5^mq\times 10^{-m}$