Hi Alexis,
3^^^3 is 3^3^3^...3 (7,625,597,484,987 copies of 3).
See:
http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation
How really big is it?
It's also Ackermann number. Its value is:
approximately 10^3,638,334,640,024.
The next Ackermann number (4^^^^4) is so large that it
could not be written on a universe-size sheet of paper,
even using exponential notation! (The "!" is not from
me.) See:
http://www.fortunecity.com/emachines/e11/86/largeno.html
"The Challenge of Large Numbers"
Another interesting article (regarding big numbers) is:
http://www.scottaaronson.com/writings/bignumbers.html
"Who Can Name the Bigger Number?"
Bye,
Suyono
prokofiev2006 wrote:
3^^^3 is 3^3^3^...3 (7,625,597,484,987 copies of 3).
See:
http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation
How really big is it?
It's also Ackermann number. Its value is:
approximately 10^3,638,334,640,024.
The next Ackermann number (4^^^^4) is so large that it
could not be written on a universe-size sheet of paper,
even using exponential notation! (The "!" is not from
me.) See:
http://www.fortunecity.com/emachines/e11/86/largeno.html
"The Challenge of Large Numbers"
Another interesting article (regarding big numbers) is:
http://www.scottaaronson.com/writings/bignumbers.html
"Who Can Name the Bigger Number?"
Bye,
Suyono
prokofiev2006 wrote:
>
> Talking about that, what do you think about this
> incredibly fast growing sequence ? :
> 0
> 1^1
> 2^^2
> 3^^^3
> 4^^^^4
> where "^" is not the usual power, but the arrow of Knut.
> The notation of Knut is defined this way:
> a^^^n = a^^(a^^(a^^�&a)) where a appears n times
>
> It then goes this way:
> 0 = 0
> 1^1 = 1
> 2^^2 = 2^2 = 4
> 3^^^3 = 3^^(3^^3) = 3^^X = 3^(3^(3^�&3)), where "3"
> appears 19683 times, (because 3^^3 = 19683).
> A giant cookie for the one who can calculate how many
> figures are in this number.
>
> Alexis
>
> PS : For those who are not afraid about heights, I can
> show another even more nauseus sequence based on
> another notation : the notation of Conway.
> PS'': we are quite far from LT, here J
>