# tohecz

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bio website kmlinux.fjfi.cvut.cz/… location Prague, Czech Republic age 27 member for 2 years, 1 month seen 10 hours ago profile views 126

Math PhD student at Czech Technical University in Prague and at LIAFA in Paris. At the same time, I'm a typesetter (and partly the copy editor) of one scientific journal (done in LaTeX, of course).

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 Nov20 comment Why do proof authors use natural language sentences to write proofs? @artem But that's partly the beauty of a non-formal proof! If you understand the proof, seeing that "showing that $2p-n>0$ is necessary" is straighforward. And if you don't understand the proof, adding this information wouldn't help. Nov13 comment Why is the absolute sign needed in the definition of a bounded function Well, or that $f(\operatorname{def} f)$ is a bounded set? :) Oct27 comment Dividing tournament into “equal” groups The world tournament is well established in the graph theory, and is connected to "each plays each" type of a game: en.wikipedia.org/wiki/Tournament_%28graph_theory%29 Oct24 awarded Curious Oct23 accepted Is this enough to prove a homeomorphism? — inverse on a dense subset Oct23 comment Is this enough to prove a homeomorphism? — inverse on a dense subset Yeah, I just realized that the problem is eventually simple, and all that needs to be said is that continuous image of a compact is a compact. Thanks for your help anyways for sure! Oct23 comment Is this enough to prove a homeomorphism? — inverse on a dense subset @JohnZHANG Sorry I was not clear. I do have a proof that in my particular case, the 3rd item is true. Oct23 asked Is this enough to prove a homeomorphism? — inverse on a dense subset Oct23 awarded Quorum Oct19 comment Questions related to maximal ideals Well, I have seen a definition of a unity in a ring as a non-zero element, which means that the zero ring is then a ring without unity. I know this is strange, but it is exactly for the reason that zero ring is too weird to be a unit ring. Oct7 comment How do I find the following definite integral? Mathematica forever? Not quite in this case :p Oct6 comment Fundamental Theorem of Calculus application It would be wise not to use $x$ for two different variables, it is very confusing. Oct3 comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$ @KyleStrand Because \bar goes before A, not after that. There's actually a red nothing after the 2nd \bar showing that an argument is missing. The correct thingy is: $\bar S \subseteq \bar A$. And I get your point. Just somehow, you can change balls to "bubbles" (arbitrarily shaped open sets) and it's the same, still keeping the idea behind. And you can even draw it like that without any need of letters -- isn't that cool? :) Oct3 comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$ @KyleStrand The point is that you first derive that $S\subset \bar A$ implies $\bar S\subset \bar A$, which is a nice, simple and completely general statement, and is somehow the core of the proof. And now, you only use this very general statement, rather than fiddling with complicated stuff as $\epsilon-d(t,s)$, from which, no true idea can be observed. Oct2 comment If $A$ is dense in $S$ and $S$ is dense in $T$ , then $A$ is dense in $T$ @KyleStrand I don't like this because it assumes a metrizable space. And while direct and "elementary", it doesn't catch the points at all, IMHO. Oct1 awarded Yearling Sep30 awarded Explainer Sep29 comment Is the perimeter of a nested convex set smaller than the containing set's? @Martín-BlasPérezPinilla Damn, my fault. Sorry for that. Sep20 comment Proof my by mathematical induction $\sum_{i=1}^{n} \frac{(-1)^{i-1}}{i} > 0$ Hello, is really your summand independent of $i$? Because currently the sum evaluates to $(-1)^{n-1}$, which is not always positive... Sep19 comment Are $10\times 10$ matrices spanned by powers of a single matrix? +1 Indeed a very nice proof by contradiction.