bio | website | math.berkeley.edu/~sramesh |
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location | Berkeley, CA | |
age | 29 | |
visits | member for | 4 years, 6 months |
seen | 22 hours ago | |
stats | profile views | 3,504 |
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.
Jul 23 |
comment |
Reconstructing the argument that yields Graham's number
@TimothyChow: The upper bound given in the paper is $f^7(12)$ where $f(n) = 2 \mathbin{\uparrow}^{n} 3$. That seems to me about exactly as easy to specify as Graham's number $f^{64}(4)$ where $f(n) = 3 \mathbin{\uparrow}^{n} 3$, so I don't know why the latter ever came up. Perhaps Graham actually tried to outline to Gardner the argument for the upper bound, and found it simpler with the weaker bound. |
Jul 2 |
awarded | Curious |
Jun 22 |
accepted | Relationship of Euler product to coprimality densities for arbitrary sets of primes |
Jun 22 |
asked | Relationship of Euler product to coprimality densities for arbitrary sets of primes |
Jun 22 |
comment |
Additivity of asymptotic density of periodic sets
Ah, nice. Here's a followup question I'm also interested in, which you will perhaps resolve with just as much ease: Suppose now we consider an increasing series of subsets $A_0 \subseteq A_1 \subseteq A_2 \subseteq ...$ of the integers, where each of these is not merely periodic but in fact of the form "Any multiple of a member of F", for some finite set F. Can the density of their union still fail to match the supremum of their individual densities? |
Jun 22 |
accepted | Additivity of asymptotic density of periodic sets |
Jun 22 |
asked | Additivity of asymptotic density of periodic sets |
May 31 |
awarded | Custodian |
May 31 |
reviewed | Approve suggested edit on Geometric interpretation for fourth coeficient of the polynomial for Hirzebruch–Riemann–Roch theorem |
May 29 |
awarded | Promoter |
May 14 |
revised |
Commuting limits in relating the harmonic series to coprimality densities
added 337 characters in body |
May 14 |
revised |
Commuting limits in relating the harmonic series to coprimality densities
added 337 characters in body |
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 |