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 Jan 20 comment Solution of integration of $e^{x^2}$ @MårtenW: I must admit I missed that, but of course this can be solved by some appropriate complex substitution. Jan 20 comment Solution of integration of $e^{x^2}$ By "elementary", we mean "elementary functions", such as taking powers and multiplying and addition. There is no expression for the integral $e^{x^2}$. We can only give it a name (specfically the "error function"). I don't know how one can prove this. Jan 15 comment Is $f = x^2$ or only $f(x) = x^2$ correct? if, by $x$, the /variable/ is meant, then I do not see how that would be incorrect. You are right however, that (in words) "plugging in a value" produces a new "value". Jan 15 comment Is $f = x^2$ or only $f(x) = x^2$ correct? So why is your view correct? Under my view, the notation is correct (albeit confusing, since I am leaving away all the isomorphisms), but under your view, it is not. Jan 15 comment Is $f = x^2$ or only $f(x) = x^2$ correct? Not quite - $x$ is not some value, but instead a variable. In that case, $x^2$ can be seen as an element of $\mathbb{R}[x]$, the ring of polynomials, which is isomorphic to a subset of the ring of continuous functions. Jan 8 comment Mathematics, Philosophy and writing. Perhaps more famous for his literature than his mathematics: Charles Dodgson / Lewis Caroll. Jan 5 comment Learning category theory before abstract algebra I think categories inherently have group-like properties, so I'd suggest you learn abstract algebra first. Though strictly speaking, neither relies on the other, so you can give it a shot. Jan 5 comment In a ring homomorphism we always have $f(1)=1$? Could you add a word on why we want to rule out such mappings? Jan 5 answered In a ring homomorphism we always have $f(1)=1$? Jan 2 comment a problem on the topological properties of a annulus Please fix ambiguous terminology: to say a map is open or closed usually refers to its graph having such properties. Jan 2 comment Are there real-life relations which are symmetric and reflexive but not transitive? Surely this relation is not reflexive for newborns... Dec 31 suggested rejected edit on Do eigenvectors always form a basis? Dec 29 comment How to prove that something is definable or not definable in a given structure?! Dear André, I am currently doing a little undergraduate research project in o-minimal structures. Thank you for showing me that this is actually something more people know about :P Dec 28 comment A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language This theorem would fail Feynman's judgement for the same reason that Banach-Tarski is not an example. Dec 27 comment Consider the sequence 01110100… Induction?[filler] Dec 26 comment The cardinality of $\mathbb{R}/\mathbb Q$ Awesome.[filler] Dec 26 comment The cardinality of $\mathbb{R}/\mathbb Q$ So why exactly are they both size continuum? Dec 25 comment Rouche's theorem So... what did you try? Dec 24 comment Studying Math, All Over Again With all due respect, Khan is not mathematics. Khan is a list of courses in passing exams. Dec 23 comment Finding $\lim_{x\to \pm\infty}f(x)$ where $a,b>0$ It's bounded from above by $(a+b)/2$