bio | website | math.berkeley.edu/~sramesh |
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location | Berkeley, CA | |
age | 29 | |
visits | member for | 4 years, 8 months |
seen | 5 hours ago | |
stats | profile views | 3,566 |
I am a graduate student in the Logic program at Berkeley, broadly interested in categorical logic and foundations of mathematics, as well as in applications of category theory to the semantics of programming languages.
May 14 |
comment |
Commuting limits in relating the harmonic series to coprimality densities
Oh, very nice, thank you. This does settle the question about the existence of the general limit, but, alas, this argument requires that we already know $\prod_{p}(1 - 1/p) = 0$, while my motivating hope remains that there is some way to noncircularly derive this fact from $\prod_{p}(1 - 1/p) = \lim_{q \to \infty} \lim_{n \to \infty} f(n, q)^{-1}$ and $\lim_{n \to \infty}\lim_{q \to \infty} f(n, q)^{-1} = 0$. |
May 14 |
comment |
Commuting limits in relating the harmonic series to coprimality densities
If I'm reading you correctly, you are saying that for sufficiently large $n$ and $q$, we have that $f(n, q)^{-1}$ is at least a quantity which tends to zero. But surely we need to show $f(n, q)^{-1}$ to be at most a quantity which tends to zero, in order to answer the last question? |
May 13 |
revised |
Commuting limits in relating the harmonic series to coprimality densities
added 15 characters in body |
May 13 |
comment |
Can the Riemann hypothesis be undecidable?
@Daniel: You're right! I haven't ruled out this possibility! All these years, sitting there unnoticed... That having been said, various sources give Robin's criterion instead as "for all $n > 5040$, $\sigma_1(n) \leq e^{\gamma} n \log \log n$.. To this, exact equality would not serve as a counter-example, and thus falsehood would entail provable falsehood. That having been said, I am not, in fact, familiar enough with the relevant material to verify whether the "$\leq$" form of Robin's criterion is genuine, or, I paranoidly worry, merely the result of careless transcription of the "$<$" form. |
May 12 |
asked | Commuting limits in relating the harmonic series to coprimality densities |
Feb 8 |
awarded | Yearling |
Jan 29 |
awarded | Notable Question |
Jan 17 |
awarded | Nice Question |
Oct 11 |
awarded | Caucus |
Sep 17 |
awarded | Nice Answer |
Jun 25 |
awarded | Excavator |
Jun 25 |
awarded | Pundit |
May 24 |
comment |
Avoiding reflexive paradox in set theory
Richard, you are coming now quite close to a principle like "Sets are given by well-founded comprehension"; this is the spirit behind ZF, and once you have that, the rest of its axioms are not far behind [you'll find that the existence of infinite sets, powersets, etc., are not automatically assured, and you may want to assure them]. |
Mar 29 |
awarded | Nice Answer |
Mar 1 |
awarded | Popular Question |
Feb 10 |
awarded | Nice Answer |
Feb 8 |
awarded | Yearling |
Dec 1 |
comment |
Application of polynomials with non-negative coefficients
Surely, the thing to do is to use q = p(1) + 1 rather than q = p(1), so as not to have to treat the case p(q) = q^n on an ad hoc basis. |
Nov 19 |
revised |
Proof without words for surface area of a sphere
added 126 characters in body |
Nov 19 |
revised |
Proof without words for surface area of a sphere
edited body |