1,604 reputation
320
bio website kmlinux.fjfi.cvut.cz/…
location Prague, Czech Republic
age 27
visits member for 2 years, 4 months
seen 12 hours ago

My former display name: tohecz

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).

Code licence details applicable on my posts on TeX.SX.

My favourite queries on SE's Data Explorer


13h
comment Is there a notation for being “a finite subset of”?
@Lehs Even though, if the fact that $A\subset B$ was particularly important and crucial for something, and not obvious at the moment in the current context, I would not hesitate much to say: "... because, from (3.14) we see that $A$ is a finite subset of $B$", or something in that manner. You are right that everything can be expressed in symbols, and it should be used as a good tool! Use symbol when appropriate, and accompany them with words when appropriate.
1d
comment Is there a notation for being “a finite subset of”?
@Lehs No notation is able to explain an important fact. Only words can.
1d
comment Is there a notation for being “a finite subset of”?
That's soooooo set-theoretical notation!
1d
comment Is there a notation for being “a finite subset of”?
@SteveJessop No. $<\omega$ is not better unless you're a set theorist. As you note yourself, $|A|<\infty$ is the most standard way of writing down that $A$ is finite, if you don't like "$A$ finite". That's what I would actually prefer myself: $A\subset B,\quad A \text{ finite}$.
Jan
21
comment Can you be 1/12th Cherokee?
@SteveJessop I know. At the same time, it's needed to say that the coins are not $100$ but rather something like $40000$, so the mean deviation is $\sim200 = 0.5%$. I just wanted to point out that it's not $23$. On the other hand, this means that you can get very precisely $1/12$ of Cherokee genes even with 2 or 3 generations considered. However, this model is far from what people have in mind with "I'm $1/8$th Cherokee", right?
Jan
21
comment Can you be 1/12th Cherokee?
@SteveJessop Needed to say: There's re-combination going on, so you receive 25% of each of your grandpa's DNA. (I'm not 100% sure on this, and a biologist should rather confirm my statement. Still, this is how I understood re-combinations.
Jan
6
comment How to stop forgetting proofs - for a first course in Real Analysis?
My favourite quote to the statistics teacher during the exam: "Excuse me, Sir, I don't remember the statement, but if you help me with it, I'll surely manage to show you the proof." Because the basic idea was that the theorem hypotheses need to be used in the proof, and that was usually enough to think out the steps.
Dec
23
comment Do we really need reals?
However, you can argue that computable numbers have sufficient completeness properties: Each computable sequence of computable numbers has a computable limit.
Dec
18
comment What is the “fastest” increasing function that's useful in some area of math?
@KlasLindbäck Please note what has been said before: Dirac's delta function does not even answer the problem: it's not a function, nor it is growing. I don't see why this answer deserves +2. IMHO the answerer should have enough judgement and delete the answer.
Dec
18
comment What is the “fastest” increasing function that's useful in some area of math?
@MJD The blog article is a perfect thing for a lecture to high school students! I really love the game that is presented there at the beginning :) (btw, (x->9^(9^x))^(9^(9^9)) (9) would be my try :) )
Nov
20
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.
Nov
13
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? :)
Oct
27
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
Oct
23
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!
Oct
23
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.
Oct
19
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.
Oct
7
comment How do I find the following definite integral?
Mathematica forever? Not quite in this case :p
Oct
6
comment Fundamental Theorem of Calculus application
It would be wise not to use $x$ for two different variables, it is very confusing.
Oct
3
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? :)
Oct
3
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.