My Number is WAYYY larger [game]

[CARuler]

(0)(2,..[10^10],2)[10]

[get_Snacked]

(0)(2^(0)(2,2,2)[10])[10]

[CARuler]

(0)(10^10,10^10,...[(0)(2,2)[10]],10^10)[10]

[rutabaga]

Where are we in FGH right now? It's been the same notation this entire page and most of the previous one but I don't understand it.

I'll go with g^81422(81422) using Stage Array Notation if that's bigger, but I have no clue how big the previous notation was.

[get_Snacked]

Where are we in FGH right now? It's been the same notation this entire page and most of the previous one but I don't understand it.

probably beyond the limit of expressibility using arithmetic-based ordinal notations.

[CARuler]

TREE((0)(10^[10]10,10^[10]10,..[(0)(TREE(3),TREE(3)[10]],10^[10]10)[10])

Where are we in FGH right now? It's been the same notation this entire page and most of the previous one but I don't understand it.

same here

[Banananananan]

TREE((0)(10^[10]10,10^[10]10,..[(0)(TREE(3),TREE(3)[10]],10^[10]10)[10])

Where are we in FGH right now? It's been the same notation this entire page and most of the previous one but I don't understand it.

same here

Transfinite omega

[confocaloid]

Where are we in FGH right now? It's been the same notation this entire page and most of the previous one but I don't understand it.

I'll go with g^81422(81422) using Stage Array Notation if that's bigger, but I have no clue how big the previous notation was.

This is one of several reasons why the entire game is inherently problematic. Other reasons include

• Not Life/CA-related.
• Too big jumps (again, "inherently problematic"). Is it really that fun to jump from something like 12 to something like 12^^^^12?
• Relatively obscure notations, where the game devolves into "who knows more obscure notations" instead of "who can define a bigger number using only available tools, while following shared ground rules".

• this thread seems to be slowly devolving into insanity

• TREE(3)

Maybe it would be more interesting with different ground rules:

• Keep things CA-related, do not just post arbitrary large numbers.
• Try to make as small jump as possible, but without relying in any way on any previously posted definition. For example, if the previous number was defined as 3^3^3, then posting "3^3^3+1" is disallowed because it obviously uses the same idea, while posting "19 x 28 x 37 x 19441 x 19927" might be allowed even though it defines the exact same number.
• Avoid using obscure notations few people understand.
• Avoid using notations you yourself don't understand.
• Avoid anything ill-defined.
• Only finite numbers.

Maybe that would go better. Or maybe that would slowly devolve into another kind of insanity.

[hotdogPi]

This is why I prefer the other game. (I can't do anything there right now because I was the last one to submit a number.)

[unname4798]

New game (Reason: Obscure notations)
10^9

[CARuler]

10^^10

[confocaloid]

10^^10

The lifespan of this pattern:

Compacted 112*89 diehard:

Code: Select all

x = 112, y = 89, rule = LifeSuper
21.8Q20.12Q4.5Q2.Q15.2M15.Q$22.Q4.Q22.Q3.2Q8.2Q.Q.4Q.Q13.2M8.2Q5.Q$
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4.M$.2W.W4.2W3.2W10.U.U3.U.U20.S8.2S12.pA.pA4.3M$.2W.W.2W2.W2.W2.W10.
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5.S15.Q4.3S10.2S18.2Q3.Q$3W4.W4.2W.2M5.M4.U7.2O2.2O4.S.S3.S.S13.Q.Q6.
S30.2Q.2Q$2W9.3W3.2M.M.M3.U.U4.3O.O.O6.S5.S9.2U3.2Q6.2S30.Q$.W3.3W5.W
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2Q.Q.Q$18.M4.M7.O4.O6.S5.S9.U.U$20.3M3.M3.2O.2O.O9.S12.2U9.M$20.2M4.M
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24.M.M.M.M2.M$28.M4.O6.3S14.U11.6M27.M.2M2.2M$28.3M12.2S6.U2.U5.U12.M
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U2.U35.3M2.3M2.M$28.M4.4M6.S4.U2.6U.U2.U3.U2.M5.M.M.2M23.3M4.Q$30.M.M
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5M3.5M3.Q.2Q$29.2M3.M.2M13.2U.U3.3U2.U3.U3.M4.2M14.2M.2M4.M.M.M5.Q$
28.M3.M4.M.M8.3U2.2U4.U3.U.U2.2M3.2M2.M.M13.2M2.2M6.MQ$30.M2.M14.2U4.
U5.3U4.U2M2.3M4.M8.2M2.2M.M8.M.Q.3Q$34.M.2M11.U.U2.3U2.U.U.5U3.2M2.M
2.M9.M3.2M.6M2.M.M6Q$34.4M10.U4.U.4U2.U.2U2.UM.M.M2.3M11.M2.M3.5Q2.2M
.2Q.Q!

Also, some yellow tubs were shifted to add an eater (it was very lucky that the eater barely misses the two boats with tails).

EDIT: And some lime tubs were added. They don't delay the fuse, but they still require two block pulls after it to clean up. The tub catalysis was another stroke of luck.

Impressive! This has a lifespan slightly greater than:

121 ^^ (121^121^121^121^121^121^121^121^121^1356648129958673823266622201465466300)

which is in turn greater than 11 ^^^ 3 in Knuth's up-arrow notation. (11 ^^^ 3 is a tighter lower bound than 121 ^^ (121 ^^ 10), as well as being more succinct. Each time we add an extra block-destroyer, that '11' will increment, until it gets to 25; the pattern stops there because 26^26 is larger than the number of loaves produced by the first fuse.)

[unname4798]

121^^121

[get_Snacked]

121^^121

less than the previous post.
121^^^121

[confocaloid]

Let f(x, y) := x * y ^ x. Then the number

Code: Select all

N := 1 + f(2,11) * f(3,11) * f(5,11) * f(7,11) = 106143875984851691911

is a prime number.
My number is N ^^^ N.

[get_Snacked]

let N_m be equal to:

Code: Select all

1 + prod(i=1)(m)(f(P_i,11))

, where P_k is the k'th prime number.
my number is N_N^^^N_N.

[CARuler]

let f(x,y)=f(x,y-1)!,f(x,0)=x
f(10^10,10^10)

[get_Snacked]

let f(x,y)=f(x,y-1)!,f(x,0)=x

FYI, this is just an iterated factorial. i'm going to change the name of this function to f2(x,y), so that confocaloid's function can be kept.
speaking of which, my number is f2(f(50,50),f(50,50)).

[get_Snacked]

let f(x,y)=f(x,y-1)!,f(x,0)=x
f(10^10,10^10)

let f(x,y)=f(x,y-1)!,f(x,0)=x

FYI, this is just an iterated factorial. i'm going to change the name of this function to f2(x,y), so that confocaloid's function can be kept.
speaking of which, my number is f2(f(50,50),f(50,50)).

actually, now that i sat on it, these numbers are most definitely smaller than N_N^^^N_N. @CARuler, please post a larger number.
(:oops: double post)

[CARuler]

let g(x,y)=x^[y](x-1)^[y](x-2)...1
then let h(x,y,z)=g(h(x,y,z-1),y), h(x,y,0)=x
then my number is h(N_N,N_N,N_N)_N

[get_Snacked]

h(N_N,N_N,N_N)_N

what does the _N mean at the end?

[CARuler]

h(N_N,N_N,N_N)_N

what does the _N mean at the end?

this:

let N_m be equal to:

Code: Select all

1 + prod(i=1)(m)(f(P_i,11))

, where P_k is the k'th prime number.
my number is N_N^^^N_N.

anways:
k(n,m)=k(n-1,m+n)*m,k(0,m)=m
mu number is:
BuseyBeaver(10^[10]10)^[k(10^[10]10,10^[10]10)]10

[get_Snacked]

h(N_N,N_N,N_N)_N

what does the _N mean at the end?

this:

let N_m be equal to:

Code: Select all

1 + prod(i=1)(m)(f(P_i,11))

, where P_k is the k'th prime number.
my number is N_N^^^N_N.

that defines N_m, not h(x,y,z)_N. i'm afraid you do not understand how sequences work.

anyways:
k(n,m)=k(n-1,m+n)*m,k(0,m)=m
mu number is:
BuseyBeaver(10^[10]10)^[k(10^[10]10,10^[10]10)]10

UNIMAGINABLY HUGE JUMP. i agree with confocaloid's statement that we should slow down the pace a WHOLE LOT.

[confocaloid]

[...]
UNIMAGINABLY HUGE JUMP. i agree with confocaloid's statement that we should slow down the pace a WHOLE LOT.

Sounds like an attempt to ascribe to me a statement that I never made, as far as I remember.

I did post something loosely related in viewtopic.php?p=199058#p199058 however I did not post there any statement containing the sequence of words "should slow down the pace a WHOLE LOT".

I think it would be better if people either made their own statements based on their position/opinion on an issue, or at least correctly quoted statements made by other people without misrepresenting their opinions/positions.

[CARuler]

Ok then,
BuseyBeaver(20)