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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 |