Talk:Graham's number

The modern mathematics detect even larger numbers, e.g. TREE(3) and SCG(13), and all these numbers have some reason in theorems and proofs, so Graham's number already is not the biggest. Ikosarakt1 (talk) 09:02, November 24, 2012 (UTC)


 * The article says that Graham's number is celebrated as the largest number used in a mathematical proof. You're right, and popular opinion is indeed wrong. Of course, we come from such an obscure corner of mathematics that there's not much we can do to change popular opinion :( FB100Z &bull; talk &bull; contribs 19:50, November 24, 2012 (UTC)

It's easy to find the last digits of Graham's number all over the Internet. A great addition to the article would be an explanation for how these digits are computed. FB100Z &bull; talk &bull; contribs 03:00, January 23, 2013 (UTC)

there will be g64. g1 is 3^^^^3 g2 is 3^...(the amount of ^ in the g2 will be 3^^^^3 which is g1.)...^3 (3^...g1 ^'s...^3) g3 is 3^...(g2 ^'s)...^3 Repeat from to the previous one till you get g64. g64 will be 3^...(g63^s)...^ Jiawheinalt (talk) 05:21, February 9, 2013 (UTC)

More formally, arrow notation:

\(a \uparrow^{1} b = a^b\) (c=1)

\(a \uparrow^{c} 0 = 1\) (b=0)

\(a \uparrow^{c} b = a \uparrow^{c-1} (a \uparrow^{c} (b-1))\) (otherwise)

And Graham's function:

\(G(1) = 3 \uparrow^{4} 3\) (n=1)

\(G(n) = 3 \uparrow^{G(n-1)} 3\) (otherwise)

Then Graham's number = G(64). This shows how easy definition can be used to create so big number. Ikosarakt1 (talk) 07:26, February 9, 2013 (UTC)

In the picture, it says that 3^^^3 = 3^^(3^^3) = 3^^7625597484987 (no problem so far) = 3^(7625597484987^7625597484987)!?!? shouldn't it be a power tower of 3's 7625597484987 high, which is far more than what it says? DrCeasium (talk) 16:53, May 19, 2013 (UTC)

You found a typo in serious mathematician article. I shall remove the photo. Ikosarakt1 (talk ^ contribs) 18:10, May 19, 2013 (UTC)
 * Nevertheless, the article has historical significance. We can, of course, point out the error. FB100Z &bull; talk &bull; contribs 19:04, May 19, 2013 (UTC)

Graham full name.
his full name is "Ronald Graham".

Sources:

Graham number is  3^[3^^^^3]^3 then 62 more times. Jiawheinalt (talk) 10:08, March 6, 2013 (UTC)

3 entry form
First, is it = to {3.5,65,1,2}?

then... {3,3,{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3{3,3}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}.

$Jiawhein$\(a\)\(l\)\(t\) 10:46, April 25, 2013 (UTC)

Graham's number is between {3,65,1,2} and {3,66,1,2}. Bowers' arrays aren't defined for nonintegers. Deedlit11 (talk) 18:12, April 25, 2013 (UTC)


 * But the 3^^^^3 is not 3^^^3. $Jiawhein$\(a\)\(l\)\(t\) 00:15, April 26, 2013 (UTC)
 * We wish they were defined. If a continuous analog were found, that would be a huge breakthrough. FB100Z &bull; talk &bull; contribs 22:12, April 26, 2013 (UTC)

Right, so Graham's number is not {3,65,1,2}, it is larger, like I said. Deedlit11 (talk) 03:07, April 26, 2013 (UTC)

There is no reasonable way to represent Graham's number in array notation. But we can bound it with {3,65,1,2} < G < {3,66,1,2}. FB100Z &bull; talk &bull; contribs 22:12, April 26, 2013 (UTC)

$Jiawhein$\(a\)\(l\)\(t\) 08:18, May 8, 2013 (UTC)

Стасплекс
Do you know that G(100) is called "Стасплекс"? Ikosarakt1 (talk ^ contribs) 09:46, June 6, 2013 (UTC)


 * Ok, lets add. Remember to put "See also". 220.255.2.158 10:46, June 6, 2013 (UTC)


 * By the way there is a mistake in this article. G1 much more than 8,7*10^185 Konkhra (talk) 10:47, June 6, 2013 (UTC).

BEAF and array
It is written that "it is reasonably close to … {3,65,1,2} in BEAF" and "There is no reasonable way to represent Graham's number in array notation", but I understand that BEAF is exactly same as array notation in that level. It looks weird that BEAF can reasonably represent and array notation cannot represent well. Kyodaisuu (talk) 22:15, December 10, 2013 (UTC)

Graham's Number = 13?
Graham's Number was originally an upper bound to a problem. The answer may be 13. No one knows but I personally guess that it's less than 20. BTD6 maker (talk) 19:39, January 28, 2015 (UTC)


 * Currently, the term "Graham's number" is given to the most well-known upper bound to this problem. But it's indeed true that the answer to the original question posed might be as low as 13. LittlePeng9 (talk) 19:43, January 28, 2015 (UTC)


 * Exoo, who proved that Graham's Solution (may as well call the answer to the original question something) was at least 11, conjectured that it was much higher, due to the fact that he could make a lot of random decisions and still find a counterexample at n=10. But I guess even 20 could be "much higher". Deedlit11 (talk) 19:59, January 28, 2015 (UTC)