Comments on: Large numbers

By: Atlas

Atlas — Sat, 26 Sep 2009 08:26:42 +0000

Forgive me for the horrible math, but this is a devious little way of showing up the original XKCD number*hence forth to be called XKCD1* Adding nothing but some simple use of up notation on Grahams number within XKCD1. I am not sure if this is a proper large number, I’m a musician not a mathematician…

A{(g64 ^^n g64), (g64 ^^n g64)}

If it is a proper large number I have soooo many college math professors to torment :D

By: Bryce H.

Bryce H. — Fri, 18 Sep 2009 20:31:13 +0000

i agree with the guy who suggested the multiple graham recursions

BB(g_g_g_g_g_g_g_g_g_g_g_g_g_99), where g_99 goes up to the 99th instead of the 64th, i don’t like busy beavers since they are both non computable and remind me of the action your mom gets on weekends, but i threw one in there just for the sake of it because hey, this mathematical pissing contest isn’t already irrelevant enough, is it?

By: Lucas

Lucas — Mon, 14 Sep 2009 04:39:23 +0000

Aleph_Aleph_Aleph_Aleph_Aleph_99

By: medyum

medyum — Thu, 30 Jul 2009 11:12:57 +0000

Its a slight variation, using F(n) as the number of iterations per recursion(or is it recursion per iteration?) leaving us room for one less nesting. i’m not sure if it is actually bigger, but to me it feels bigger… plus the algebra hurts more.

By: now I'm less drunk than I was

now I'm less drunk than I was — Thu, 02 Jul 2009 03:51:04 +0000

I was pretty faded last night when I posted the above (as “DaOG”), and I think tangent might not have been what I meant. Anyway, I think it’s more elegantly stated as:

1/pi_R

So does that compete w/ the busy beavers, or no?

By: DaOG

DaOG — Wed, 01 Jul 2009 11:12:22 +0000

The WTFBIGNUM function:
I define fWTFBIGNUM=tan(({pi}-{pi_R})/{pi})
where,
{pi_R}= The RUTHERFORD QUANTITY = that fraction equal to the remainder of PI after (ya kno; comprised of the decimal to the right of) the first string of digits of PI (as evaluated in base 10 numerals) identical to a fully worked out expression of the string of digits representing Graham’s #.

If that made sense, can someone knowledgeable on the subject tell me if I won?

By: metroid composite

metroid composite — Tue, 28 Apr 2009 22:30:49 +0000

Just read this a couple minutes ago. Umm…as far as

H(n)=BB^n(n);H(H(H(H(H(H(9))))))

That can be improved on pretty easy with using all the same notation:

H(n)=BB^n(n);I(n)=H^n(n);I(I(9))

So…two-layer simple recursion on BB. Obviously bigger since I(9) = H(H(H(H(H(H(H(H(H(9))))))))). There’s not really enough space in 32 characters to define a nonsimple recursion on BB without it looking ugly, though.

By: Anonymous

Anonymous — Sun, 22 Feb 2009 23:24:33 +0000

23!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111one

and so on

By: Joseph

Joseph — Thu, 04 Dec 2008 04:47:58 +0000

Well, I’ve decided to put together a list of positive integers in sequential order. Unfortunately, I had to leave out a few in order to reach the level of some of the numbers being discussed here.

The first Ackermann number
2
3
The second Ackermann number
5
10
20
40
80
500
4000
BB(5)
googol
googolplex
A(4, 2)
A(4, 4)
The third Ackermann number
3????3 (g_1)
Graham’s number (g_64)
g_65
g_99
g_googol
A(g_64, g_64)
BB(g_64)
H(n)=BB^n(n);H(H(H(H(H(H(9))))))
f=BB;^^^^^^^^^!9f9f9f9f9f9f9f9f9
The smallest number bigger than any number that can be named by an expression in the language of first order set-theory with fewer than a googol (10^100) symbols.

I didn’t use many of the numbers being discussed here; there were only two that I saw that seemed to be worth mentioning. One was, of course, Randall’s. The other uses prefix notation, which I’d say is an excellent way to go about this.

By: scikidus

scikidus — Sat, 29 Nov 2008 01:57:14 +0000

I feel like I’m going to have to agree with the idea that doing something like applying a tangent to a number incredibly close to pi/2 rads is the best option here.

However, tan was not my first choice; instead, what if Riemann’s zeta function was invoked? (It’s represented with ?(s), so it takes up less chars than “tan” does.) You could build the closest number to 1, something like this:

scikidus’ Number = F(x)=?(1-(1/ggx!));F^F(G)(ggG)

where gx is the xth Graham’s number, and G is Graham’s Number, which = g64.

Does anyone know which function increases more quickly as it approaches its respective asymptote?

And is my number big enough?