Timeline for Reconstructing the argument that yields Graham's number
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2017 at 17:46 | comment | added | Sridhar Ramesh | It's not known that $f^{63}(4)$ is not large enough. Indeed, for all we know, 13 [that is, the number 13, in itself] may be large enough (and for all Graham knew at the time, 6 may be large enough). But, at any rate, he was able to show that $f^{64}(4)$ was definitely large enough. I don't know the argument, but presumably, this was some random thing he could relatively easily show large enough, by an argument that did not immediately apply just as well to $f^{63}(4)$. | |
| Jun 30, 2017 at 11:29 | comment | added | Paul Smith | @SridharRamesh - it it easy to show that f63 is not large enough, and that f64 is? | |
| Jul 23, 2014 at 1:30 | comment | added | Sridhar Ramesh | @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. | |
| Jan 12, 2013 at 1:19 | comment | added | Toby Bartels | But (at least if Timothy's question on this thread is answered) it does appear naturally in a watered-down version of a proof intended for popularisation. | |
| Jan 11, 2013 at 23:15 | comment | added | Brendan McKay | So we should stop referring to it as a number that appears naturally in a proof. | |
| Jan 11, 2013 at 19:55 | vote | accept | Timothy Chow | ||
| Jan 11, 2013 at 19:55 | comment | added | Timothy Chow | Interesting! Thanks. I just took another look at Graham and Rothschild's paper and there might still be an interesting question here. Namely, given that you want to write down a number using Knuth's arrow notation that is bigger than the upper bound in the paper, would you be fairly naturally led to write down Graham's number? It's not immediately obvious to me. | |
| Jan 11, 2013 at 18:08 | comment | added | Andrés E. Caicedo | John's Google+ post on Graham's number: plus.google.com/117663015413546257905/posts/KJTgfjkTZCQ | |
| Jan 11, 2013 at 18:06 | history | edited | Andrés E. Caicedo | CC BY-SA 3.0 |
deleted 4 characters in body
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| Jan 11, 2013 at 17:26 | history | answered | John Baez | CC BY-SA 3.0 |