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Set bounties
 Apr 27 awarded Good Answer Aug 30 awarded Necromancer Jan 5 awarded Popular Question Dec 4 awarded Nice Answer Nov 8 comment Pseudonyms of famous mathematicians If you mean by Al-Khoresmi "Abu Ja'far Muhammad ibn Musa Al-Khwarizmi" then I think he does not qualify. It was customary at the time to use geographic names of family origin as family name. This means that he had the name "Al-Khwarizmi" all his life and that his father, brothers and sons (if he had any) had the same name. Nov 8 answered Pseudonyms of famous mathematicians Nov 3 comment Cardinalities larger than the continuum in areas besides set theory For the example of measurability I would say it is still within the realm of set theory (descriptive set theory). I think there are results on infinite dimensional topology that require a space of very large cardinality, but the ideas and techniques are borrowed from model theory. Actually it seems that whenever we study questions of infinite cardinals we require tools from model theory or set theory. Oct 30 awarded Commentator Oct 30 comment Question about Schauder bases in C([0,1]). The usual example in $C([0,1])$ is $\vert t-\frac 12\vert$. Its Fourier series does not converge uniformly. Oct 30 comment Question about Schauder bases in C([0,1]). Actually if a trigonometric series converges uniformly to a function $f$, then the series must be the Fourier series of $f$. This is statement 1.41 on page 6 of Zygmund's {\it Trigonometric Series}. Oct 28 comment describe subsets of the integers closed under the binary operation Ax+By Wouldn't $(1)$ be the set of all integers of the form $F(A+B)$ where $F$ is a polynomial with positive integer coefficients? Oct 27 comment two sequences whose difference converges to zero Yes. I thought it may suggest a suitable terminology. Oct 27 answered two sequences whose difference converges to zero Oct 27 answered “Riemannâ€“Stieltjes derivative”? Oct 27 comment “Riemannâ€“Stieltjes derivative”? The existence of the Radon-Nikodym derivative requires that the measure $dF$ be absolutely continuous with respect to Lebesgue measure which is not satisfied by a pure jump function where the support of the measure is a finite or countable set. Oct 26 revised What numbers can be approximated “pretty well” by rationals? added 1 characters in body Oct 26 accepted The dual group of $\mathbb Q$ Oct 26 comment Wonderful applications of the Vandermonde determinant Another application is to prove that for any $0<\alpha_1<\cdots<\alpha_n$ the family $$\sin \alpha_1x,\cdots,\sin\alpha_nx$$ is linearly independent in $C^{4(n-1)}(\mathbb R)$. Oct 25 answered What numbers can be approximated “pretty well” by rationals? Oct 15 comment Does constructing non-measurable sets require the axiom of choice? There is an interesting discussion on: math.niu.edu/~rusin/known-math/99/AD_AC