Thanks for the articles Suyono, very interresting.
But I'm afraid 3^^^3 is much bigger than 10^3,638,334,640,024.
The number of digits can be calculated this way, if I'm not mistaken:
Log10(3^^^3) = log10(3) * log3(3^^^3)
= 0,477 * (3^(3^(3^�&3))), where 3 is repeated 7,625,597,484,987-1
times.
That's HUGE !
And the googolplex can go cry in his mother 's skirt.
An enormous step for a man's mind, and yet a tiny step for infinity
Alexis
But I'm afraid 3^^^3 is much bigger than 10^3,638,334,640,024.
The number of digits can be calculated this way, if I'm not mistaken:
Log10(3^^^3) = log10(3) * log3(3^^^3)
= 0,477 * (3^(3^(3^�&3))), where 3 is repeated 7,625,597,484,987-1
times.
That's HUGE !
And the googolplex can go cry in his mother 's skirt.
An enormous step for a man's mind, and yet a tiny step for infinity
Alexis
--- In [email protected], Suyono <suyonohy@...> wrote:
>
> 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:
> >
> > 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
> >
>