Reputation
16,103
Next privilege 20,000 Rep.
Access 'trusted user' tools
Badges
1 20 59
Newest
 Yearling
Impact
~215k people reached

20h
revised limit point of a set under discrete topology
added 13 characters in body
1d
answered limit point of a set under discrete topology
1d
comment Construction of factor groups
@PhucNguyen: Yes. That is, more or less, the content of that statement.
2d
awarded  Yearling
Apr
15
comment Hausdorff Maximal Principle
I disagree. The restricted form is more complicated to state. And besides, Zorn's lemma which is both (a priori) weaker and more complicated is way more commonly used than HMP (because it is more convenient to use, I guess), so this does not amount to much.
Apr
15
answered Calculate $p$-adic metric
Apr
13
awarded  Enlightened
Apr
8
revised $X$ is completely regular iff it carries the initial topology w.r.t. $C(X,\mathbb{R})$
added 108 characters in body
Apr
8
answered $X$ is completely regular iff it carries the initial topology w.r.t. $C(X,\mathbb{R})$
Mar
24
comment Solving a system of equations with 3 variables in under a minute
@YoTengoUnLCD: Your question does not make sense. The way I read it, is that suppose we have $x,y,z$ which satisfy these equations. It clearly follows that $3(x+y+z)=17$. With your question, the assumption is false. If it was the case with the system in question, you could argue that every answer is true (by principle of explosion).
Mar
24
comment Why are turns not used as the default angle measure?
From what I've heard from my physicist colleagues, they frequently assume that all constants are equal to $1$, including $\pi$.
Mar
24
answered Let F be a finite field of characteristic $p$. Show $f(a) = a^p$ is a ring homomorphism, injective, and surjective
Mar
24
comment Help on notation: $\mathbb{Z}/n\mathbb{Z}$ vs. $\mathbb{Z}_n$
This was mentioned in a comment to the original question. Five years ago, ten minutes after the question was posted.
Mar
24
comment Given $\Bbb N$ can you reach every infinite cardinal by performing succesive power set operations?
@AndresMejia: I don't see how that is relevant at all.
Mar
22
comment Discrete subgroups and Discontinuous subgroups of the isometries of the euclidean plane
The general definition of a proper group action (for non-discrete groups) is that the action is proper if the map $G\times X\to X\times X$, where $(g,x)\mapsto (gx,x)$ is proper, i.e. closed, and preimages of points are compact. (If $G$ is discrete, this is equivalent to the one you have cited.) By the way, you forgot to say that $x\neq y$ in the definition of discontinuity.
Mar
21
awarded  real-analysis
Mar
18
comment Terry Tao, Russells Paradox, definition of a set
@PeterLeFanuLumsdaine: Sure, but even if the fully formalised terms are fully human-readable in principle, I very much doubt a human (well, an ordinary mathematician, anyhow) could understand a nontrivial reasoning (completely, not locally) without first translating it back into the not-strictly-formal language. Principia was just an example. Modern systems seem to have very much the same faults: proofs of simple facts (like famous $1+1=2$ in Principia) take inordinate amount of space, while proofs of really complicated facts seem to be infeasible. I'd like to be contradicted, though.
Mar
17
answered Terry Tao, Russells Paradox, definition of a set
Mar
13
comment Are $B_1(0)$ and $B_1(0) \setminus X$ homeomorphic?
@goblin: So that the obvious function (scaling radially with respect to center) is continuous. Or if you are asking about the tip of the cone, it's the same as the end of $X$.
Mar
12
comment What is $K^n$ when $K$ is a field?
I'm no algebraic geometer, but I've seen people write ${\bf A}^n$ to mean the scheme (as opposed to the set $n$-tuples).