Mark S.
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 Jan 22 awarded Revival Jan 22 answered Is there a metric space where 2 + 2 = 5? Jan 22 awarded Revival Jan 18 comment Definition of topological space: Is Ω equal to the powerset of X? @leftaroundabout The indiscrete/trivial topology also is in some sense "behaving as a plain old set". Both are adjoints to the forgetful functor that forgets about topological structure: ncatlab.org/nlab/show/discrete+and+codiscrete+topology Jan 16 comment Why are sets like $\{x \in \mathbb{Q}|-\pi < x < \pi\}$ both closed and open in $\mathbb{Q}$? @FemaleTank, There are two different topologies being discussed. One is "balls contain all the real numbers they should", but the other, the one in which the set is both open and closed, is "we only include the rational numbers in any considerations". Jan 16 revised Is there a relationship between isometry as defined on metric spaces and those on vector spaces? changed tag from vector space isomorphism to category theory, as that seems to an agreed topic Jan 16 answered Is there a relationship between isometry as defined on metric spaces and those on vector spaces? Jan 16 comment Notation of the second derivative - Where does the d go? @IwillnotexistIdonotexist First, it destroys the nice "multiplication" of factors of the form $\frac{\partial}{\partial x}$ by saying something like "$\partial\partial=\partial^2$ on top, but $(\partial x)(\partial y)=\partial xy$ on bottom". More importantly, IMO, is the fact that, in general: $\frac{\partial}{\partial x}$ and $\frac{\partial}{\partial y}$ don't commute, but $x$ and $y$ do. So to use the notation you proposed would require that $\partial xy$ in a denominator can't be replaced with $\partial yx$, even though in all other real-anaylsis contexts $xy\to yx$ would be fine. Jan 16 comment Notation of the second derivative - Where does the d go? @IwillnotexistIdonotexist I don't think I've seen a multivariable calculus book that does that. I've only seen books write things like $\partial x\partial y$ in the denominator, and I believe for good reason. Jan 14 comment Having $\pi$ fingers and count Your question is more or less answered at math.stackexchange.com/questions/1465617/… Jan 13 comment Trouble with Discrete Math proof Certainly, $A>B>0$ always implies $A>0$. But does that mean it can't also imply $A\le0$? Jan 13 comment Trouble with Discrete Math proof The statement given in the problem is true, not false. Justin has written the reason why in a comment in his question. Jan 13 comment Trouble with Discrete Math proof Daniel, you may want to reread the whole statement. @Justin, that's not quite the contrapositive. Jan 13 comment Trouble with Discrete Math proof Have you tried sketching a graph of $n$ and $n^2+1$? Jan 12 revised What's between the finite and the infinite? added infinity tag Jan 11 comment Definition: Mathematical way to define the “left” and the “right” @TonyK, it was definitely Feynman. Do a search for the text: Extend your right hand,” you say, to which the alien responds, “What is right Jan 6 comment Terminology for a game in which Black and White have the same “probability” to win of course, that's a fine definition of nonpartisan, and applies here. If this were English.SE, I wouldn't have said anything; I just wanted to warn people interested in the mathematical study of these games that that word in particular may lead to confusion. Jan 6 comment Terminology for a game in which Black and White have the same “probability” to win Nonpartisan might be confused for the technical terms "impartial" or "not partizan" in combinatorial game theory. Jan 6 answered Terminology for a game in which Black and White have the same “probability” to win Jan 3 comment A map from $(0,1)$ to $(0,1)$ such that the image of every open interval in $(0,1)$ is $(0,1)$ This reminds me a lot of Conway's base 13 function.