My number is bigger!

"My number is bigger!" was a contest held in a discussion thread at the now-defunct xkcd forums. The thread was begun on the 7th of July, 2007, and as of October 2018, it consists of 1589 posts.
The goal of the contest is to come up with a finite, well-defined number bigger than the last poster's number, by using already established numbers and notations (such as Graham's number and xkcd number) and without referring directly to the previous number. Another rule is that all numbers must be "computable" — that is, their definition must only employ computable functions.
==Valid entries==
===Page 1/40:===
====User: gmalivuk====
Number: 9,000
Size:9*103
Time as biggest number: July 7, 2007 7:20 pm UTC - July 7, 2007 7:25 pm UTC
====User: LE4dGOLEM====
Number: What Vegeta's scouter said about Goku/Kakarot's power level. (Ill-defined)
Size: >9000 - >8000 depending on the version of the scene used
Time as biggest number: July 7, 2007 7:25 pm UTC - July 7, 2007 8:57 pm UTC In the case of >9000 because 9001>9000 But never in the case of >8000 because 9000>8001
====User: Twasbrillig====
Number: 32507925092532526327561017283413824652374
8638245712364831206832587263418725404501384532106434321
8561328401512834613284108275451257632185610328418032476
3218065230850123857632105612086532150632150623199231659
9123659812364982364551456072357032165237165213078423145
2137486328042384512461098234684583641284321061273408164
2309452139562982309126570932156013297541239060129346321
0974623170523165092361507612093753209843261897432980213
6471265092437981075610298127657632109562135976231507896
12359817234763217562310947231984654761253908216507486502937521093865.
Size: Lower bound: 10^548, Upper bound: 10^549
Time as biggest number: July 7, 2007 8:57 pm UTC - July 7, 2007 9:04 pm UTC
====User: crazyjimbo====
Number: 568390125739205684705612809352167456489132749013265712367432
718953216987051326795312659012367567218920165701897342905621
746312089234798162348902357390216705163290561325071326479012
36439210609321457923106512390756219032892659312549032461804
372160123482146385486432890164215483240823684731254132487031
256173256123075327065415546328946321895632199561329913260512
3605123568021650123675832105803256081236742308148230165812367
5215457280148231643821510482316581234346012354831054045278143
62785238602138463217542836847325642831438271016572362523529052970523. (The previous number backwards.)
Size: Lower bound: 10^548, Upper bound: 10^549
Time as biggest number: July 7, 2007 9:04 pm UTC - July 7, 2007 10:03 pm UTC
====User: Twasbrillig====
Number: 568390125739205684705612809352167456489132749013265712367432
718953216987051326795312659012367567218920165701897342905621
746312089234798162348902357390216705163290561325071326479012
36439210609321457923106512390756219032892659312549032461804
372160123482146385486432890164215483240823684731254132487031
256173256123075327065415546328946321895632199561329913260512
3605123568021650123675832105803256081236742308148230165812367
5215457280148231643821510482316581234346012354831054045278143
627852386021384632175428368473256428314382710165723625235290529705231. (The previous number but with a one at the end.)
Size: Lower bound: 10^549, Upper bound: 10^550
Time as biggest number: July 7, 2007 10:03 pm UTC - July 7, 2007 10:07 pm UTC
====User: une see====
Number: 999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
Size: Lower bound: 10^1439, Equal to: 9[1440] in Copy notation Upper bound: 10^1440
Time as biggest number: July 7, 2007 10:07 pm UTC - July 7, 2007 10:17 pm UTC
====User: Twasbrillig====
Number: 999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999a in hexadecimal.
Size: Lower bound: 16^1439~10^1732, Upper bound: 16^1440~10^1734
Time as biggest number: July 7, 2007 10:17 pm UTC - July 7, 2007 10:27 pm UTC
====User: Blatm====
Number: a66666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666
666666666666666666666666666666666666666666666666666666666666 (The previous number upside down.)
Size: Lower bound: 16^1439, Upper bound: 16^1440
Time as largest number: July 7, 2007 10:27 pm UTC - July 7, 2007 10:45 pm UTC
====User: gmalivuk====
Number: 10^(10^10)
Size: Lower bound: Trenanillion, Equal to: Trialogue, Upper bound: Duonanillion
Time as largest number: July 7, 2007 10:45 pm UTC - July 7, 2007 11:52 pm UTC
====User: Rodan====
Number: 10^(10^(10^10))
Size: Lower bound: Gigillion, Equal to: Tetralogue, Upper bound: Googolplexithrong
Time as largest number: July 7, 2007 11:52 pm UTC - July 8, 2007 7:13 pm UTC (long gap was due to a few valid submissions getting deleted)
====User: Twasbrillig ====
Number: 10↑↑512
Size: Lower bound: Bighol, Upper bound: Chilialogue
Time as largest number: July 8, 2007 7:13 pm UTC - July 8, 2007 8:26 pm UTC
====User: gmalivuk====
Number: 10↑↑↑3
Size: Lower bound: Megafugagargantugoogolplex, (Best name for a number ever.) Equal to: Tria-taxis, Upper bound: Doovolplex
Time as largest number: July 8, 2007 8:26 pm UTC - July 8, 2007 8:58 pm UTC
====User: Blatm====
Number: 3↑↑↑10
Size: Lower bound: Binary-toodcol Equal to: Ternary-toodcol Upper bound: Giggoloctoplex
Time as largest number: July 8, 2007 8:58 pm UTC - July 9, 2007 8:50 pm UTC
====User: xooll====
Number: 4↑↑↑10
Size: Lower bound: Ternary-toodcol, Upper bound: Giggoloctoplex
Time as largest number: July 9, 2007 8:50 pm UTC - July 9, 2007 10:42 pm UTC
====User: Ended ====
Number: (10↑↑↑10)!
Size: Lower bound: Deka-taxis, Upper bound: (10↑↑↑10)^(10↑↑↑10)
Time as largest number: July 9, 2007 10:42 pm UTC - July 9, 2007 10:59 pm UTC
====User: Twasbrillig====
Number: (10↑↑↑↑↑↑↑↑↑↑10)! x (10↑↑↑↑↑↑↑↑↑10)!↑↑↑↑↑↑(10↑↑↑↑↑↑10)!
Size: Lower bound: Tridecal Upper bound: Deka-dodekaxis
Time as largest number: July 9, 2007 10:59 pm UTC - July 9, 2007 11:42 pm UTC
==== User: Blatm====
Number: (10↑↑↑↑↑↑↑↑↑↑10)! x (10↑↑↑↑↑↑↑↑↑10)!↑↑↑↑↑↑(10↑↑↑↑↑↑10)! in base 11 (The previous number but in base 11)
Size: Lower bound: Tridecal Upper bound: Deka-dodekaxis
Time as largest number: July 9, 2007 11:42 pm UTC - July 10, 2007 1:59 am UTC
====User: gmalivuk====
Number: 3→3→3→3
Size: Lower bound: Yudkowsky's Number (Saibian) Equal to: Conway's Tetratri Upper bound: Kudi-Chan's Number
Time as largest number: July 10, 2007 1:59 am UTC - July 11, 2007 10:18 am UTC
===Page 2/40===
====User: Mouffles====
Number: "Define a function f:
f(1)=1
f(2)=2→2
f(3)=3→3→3
etc.
Then the number is f(f(...f(g_64)...)), where the function is applied g_64 times."
Time as largest number: July 11, 2007 10:18 am UTC - July 14, 2007 10:28 pm UTC
====User: warriorness====
Number: Define a function Q such that Q(x) is x→x→...x, where the number of arrows in that sequence is equal to x→x→...x, where there are x arrows in that second chain.
Now define W(x) = Q(Q(...Q(x)...) so there are Q(x) number of "Q"s in there.
My number is: W((g_64)!)
Time as largest number: July 14, 2007 10:28 pm UTC - July 15, 2007 4:42 am UTC
====User: Mouffles====
Number: 
Let f1(x) = x→x→...→x, with x x's, as in my previous number.
Now let f2(x) = f1(f1(...f1(x)...)), where f1 is applied f1(x) times.
Then let f3(x) = f2(f2(...f2(x)...)), where f2 is applied f2(x) times.
etc.
My number is f g_64(g_64)
Time as largest number: July 15, 2007 4:42 am UTC - July 22, 2007 10:57 pm UTC
==== User: ijmaxwell====
Number: I define a sequence of sequences:
a(0)(n) = n→.....→n (with n→n occurrences of n)
a(m)(n) = a(m-1)(a(m-1)(....(a(m-1)(n))....)) (with a(m-1)(n) nested occurrences of a(m-1))
Define b(0) = a(Ack(G,G))(Ack(G,G)), where Ack is the Ackermann function and G is Graham's number.
Define b(n) = a(b(n-1))(b(n-1)).
My number is b(Ack(G,G))
Time as largest number: July 22, 2007 10:57 pm UTC - Dec 7, 2008 10:15 pm UTC (I know.)
=== Page 3/40===
====User: Actaeus====
Number:
So, here's my try:
First, we have a→2 b, defined as a→a→...→a→a with b occurrences of a.
This expands the same way Conway's notation does, so X→2a→2b = X→2(X→2...→2(X)→2b-1)→2b-1)....) with a occurrences of X.
So your a(0)(n) is the same as n→2 nn.
Next, we add a→3 b = a→2a→2...→2a→2a, again with b a's. You can see where this is going.
a(m)(n) is large, but it's smaller than n→10
 m. This is because recursion is pitifully weak next to the kind of 
extension Conway's and my arrows can do. Remember, this is n→9n→9... with m occurrences of n. It's impossible to comprehend how many occurrences of n you have once you get to →8,
 for reasonably large m. Think about how high a power tower is for 
3→3→3→3→3→3→3. You can't. It's too large. Much better than 
3→3→(3→3→(3→3→3)), which is just recursion. And that's just 3→27. 
By
 the time my arrows get down to normal Conway notation, there are too 
many to describe without my own new notation. Regular arrows are no 
longer relevant. So, I can't prove it, but (given the ridiculous power 
of extending arrows, compared to recursion, and given how many arrows 
you get here) I believe ijmax's number is much smaller than 3→A(G,G) 4.
But I'm not satisfied....yet.
I have to be absolutely sure, so let's define a→2 b to be a→b a.
This is extended in a way similar to Conway's arrows, butX→2 0 = X because x→2 1 = x→x 
Now it gets really fun. a→2,2 b = a→b2 a.
To clarify, that's a→2a→2...→2a, with b occurrences of a. This is insanely big. It's insane even compared to a→A(G,G) b.
And a→2,n b is a→b2,n-1 a.
Now, these numbers are already thread-killers, but I'm not done.
a→3 b = a→2,b a. Once again, this is extended just like Conway arrows but with 0 instead of 1 being the vanishing number.
a→3,1,2 b = a→b3 a.
a→3,1,n b = a→b3,1,n-1 a.
a→3,2 b = a→3,1,b a
a→3,2,n b = a→b3,2,n-1 a
a→3,3 b = a→3,2,b a
a→3,n b = a→3,n-1,b a
a→4 b = a→3,b a
a→4,1,1,2 b = a→b4 a
a→4,1,1,n b = a→b4,1,1,n-1 a
I think you get it, somewhat. Remember: the subscripted list is length N, where N is the first number, but trailing 1's are removed.
The last number adds a superscript b, and decrements. All other numbers decrement and set the following number equal to b, but you only use them after the rest of the list is gone because they've reached 1.
These numbers are too big to talk about in the same context as any previous ones.
Now, to end this craziness, define a function ↻(a) = a→a a
MY NUMBER: ↻(A(G,G))
Time as largest number: Dec 7, 2008 10:15 pm UTC - Dec 8, 2008 11:35 pm UTC
==== User: scikidus====
Number: Let F(X) =   / X X X X X … X X X X X \ 
             /  X X X X X … X X X X X  \ 
            /   X X X X X … X X X X X   \ 
           /    X X X X X … X X X X X    \ 
          /     X X X X X … X X X X X     \ 
         |      | | | | | \ | | | | |      | 
          \     X X X X X … X X X X X     / 
           \    X X X X X … X X X X X    / 
            \   X X X X X … X X X X X   / 
             \  X X X X X … X X X X X  / 
              \ X X X X X … X X X X X /  
with X columns and X rows in those brackets. F(X) is in BEAF.
Borrowing numbers from my previous entry,
Let H(x) = zeta(1+(1/g(g_(x!)!)!))
Y = H^H(g_g_g_...[H(g_g_g_xkcd!) sub-levels of g_ here]..._g_g_(H(g_g_g_xkcd!)))(g_g_g_...[H(g_g_g_xkcd!) sub-levels of g_
 here]..._g_g_(H(g_g_g_xkcd!)))
Where
g_x is the xth number in the Graham's number sequence, and
xkcd is Randal Munroe's xkcd number, equal to Ack(g_64,g_64)
My number is equal to FY(Y), or F(Y) applied recursively Y times.
==External links==
*My number is bigger! (via Wayback Machine)
Category:Contests