tomasz
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 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).