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 Feb 2 comment Circle is similar to a polygon with infinite number of sides @Kaster And I prefer it to be considered not as a limit, but as a "real" polygon with infinite number of sides. For example in complex number theory the infinity is not just a limit of finite values, but a quite particular point of Riemann sphere. Feb 2 comment Circle is similar to a polygon with infinite number of sides @Kaster I know that it is a limit. But what is the topology and what is the filter on which the limit is taken? Nov 20 comment Name of the class of maps between posets such that $f(x)\le f(y)\implies x\le y$ Oh, if the implication holds also in the reverse direction, it is an order embedding. This is probably what I need Oct 10 comment Locally monotone function is monotone I don't get why $I$ must be a $\sim$-class Oct 10 comment I don't understand why we represent functions $f:I \subseteq \Bbb R \to \Bbb R^2$ the way we do. Also note that for 1-argument functions the image is usually just an interval on the real line, not an interesting set. For this reason interesting images (such as parametric curves) usually appear for 2-argument (or more arguments) functions. This was the exact reason of your confusion, when you switched from 1-argument to 2-argument functions Oct 8 comment Another conjecture about $C^1$ integral curves Probably we can build a counter-example based on $f(x) = \begin{cases}x^2\sin{(\tfrac{1}{x})} & \mbox{if }x \neq 0, \\ 0 &\mbox{if }x = 0\end{cases}$ from en.wikipedia.org/wiki/Smoothness Oct 8 comment Prove (in an abstract setting) that a function is right differentiable and the right derivative is continuous Another similar conjecture: math.stackexchange.com/questions/1470877/… Oct 6 comment Two ways to describe image of a filter under a function "minus" -> "minutes" in my previous comment Oct 6 comment Two ways to describe image of a filter under a function Hm, I spent around ten minus trying to prove this, yet without success. I expected it to be easier. Any proof (not only the shortest one) would be helpful Oct 6 comment Two ways to describe image of a filter under a function I wonder that Google for ("filter image" | "image of filter") function set "filter base" does not find relevant enough results Sep 21 comment Defining a Nested Tree (set-theoretic) en.wikipedia.org/wiki/Tree_%28graph_theory%29 Sep 19 comment Restricting a natural isomorphism Also note that I misunderstand something related with this: en.wikipedia.org/wiki/… Sep 19 comment Restricting a natural isomorphism It seems that you have misunderstood my question (or rather that I asked it wrongly). I have edited the question. Does your thesis hold nevertheless? Sep 18 comment non-atomic complete Boolean lattice Please explain what "mod out" means Sep 16 comment Another probability combinatorics problem inspired by Bible @MichaelHardy It seems that I have forgotten school biology. You are right (accordingly what I've read on the Web after your note), parts of chromosomes recombine (however this happens in egg and sperms cell when they are formed, not when they "merge"). This renders my entire idea completely wrong. However, a mathematical wordproblem remains valid Sep 16 comment Another probability combinatorics problem inspired by Bible @MichaelHardy I am not a biologist, but as far as I know, individual genes in a chromosome are always present together. In other words, a chromosome is never split in lesser parts (such as genes). So your point is not valid Sep 16 comment Another probability combinatorics problem inspired by Bible @Titus Thanks, this was my error, I've edited the question Sep 16 comment Another probability combinatorics problem inspired by Bible @Titus This was already considered in comments to my first question math.stackexchange.com/questions/1438565/… Aug 6 comment Notation about commutative diagrams and their vertices @RobArthan But I need to explicitly refer to different vertices in my proof text. Well, maybe I should just say like "top right" node of the square diagram? Aug 6 comment Notation about commutative diagrams and their vertices Well, what's about $0[A]\overset{f}{\leftrightarrow} 1[A]$ or $A[0]\overset{f}{\leftrightarrow} A[1]$?