GRAHAM'S NUMBER

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Definition of Graham's Number:

x ^^(1) y = x ^ y
(Normal exponentiation)

x ^^(n) y = k_n(y)
(^^ is a function which returns an operator)

k_n(1) = x
k_n(t) = x ^^(n-1) k(t-1)

G(1) = 3 ^^(4) 3
G(n) = 3 ^^(G(n-1)) 3

Graham's Number = G(64)


Examples of the ^^(n) notation:

3 ^^(1) 3 = 3 ^ 3 = 9

2 ^^(2) 4 = 2 ^ 2 ^ 2 ^ 2 = 2 ^ 2 ^ 4 = 2 ^ 16 = 65536

5 ^^(2) 3 = 5 ^ 5 ^ 5 = 5 ^ 25 = 298023223876953125

2 ^^(3) 3 = 2 ^^(2) 2 ^^(2) 2 = 2 ^^(2) 2 ^ 2 = 2 ^^(2) 4 = 65536 (from second example)

Category:

Education

Tags:

• big
• number
• graham
• math
• biggest
• insane
• crazy

[Rpodnee]

Only watching this because I couldn't determine your gender from the thumbnail and wanted to challenge my guessing skills. I lost!

[Mozza314]

@Rpodnee Goodbye troll. Go jerk off to getting another person to block you.

[swygster]

How would one use numbers of this size in a mathematical scheme? Infinity will always be the largest value of anything, even greater than any unit in the universe if the universe theoretically kept expanding for eternity. But Graham's number is still finite regardless, but it's freakin' unbelievably finite. Infinity is more of a concept than a number, but does this mean that Graham's number is also a concept; but in a different way?

[Mozza314]

@swygster Graham's number is as much a number as 1, 2, or 3. Graham's number was proven to be an upper bound to a problem.

[MrKasey361]

"Suppose you say 'Graham's number +1' ...Well then you would be an annoying motherfucker!" BAHAHA XD

Seriously though...this video didn't explain the "power tower" notation, so it was practically useless, but it was funny as hell anyway. XD

[Mozza314]

@MrKasey361 Yeah well, that was the intention :-P.

[JustinFromSydney]

You know whats bigger than Graham's number?

My penis.

[somethingblue22]

meameamealokkapoowa oompa is bigger than G64 :D

[somethingblue22]

i thought of a googolpluxian .. :D ur funny though lol

[djbarcode5xyz]

Okay, here's how it goes: You've got a googol, then a googolplex, then Graham's Number, then infinity, then Chuck Norris' dick!

[sirjezzumz]

Grahams number to the power of graham. I just created sirjezzumz's number.

[carlschwenke]

i win



[carlschwenke]

10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10(10(10(10(10(10(10(­10(10(10(10)grahamed

[vwerlingyahoocom]

@JustinFromSydney LOL.

[NarwhalCannonball]

Wait, how is the observable universe 156 billion lightyears in diameter?

Since the universe is some 14 billion years old, shouldnt the observable universe be like 28 billion lightyears in diameter?