Hi Alexis,
Thank you for the correction. Yes, you are right.
That article ("The Challenge of Large Number") was in
Scientific American. I didn't notice that when it says
Ackermann numbers (at the end of article); it means
DIFFERENT Ackermann numbers. It's 3^^4,
not 3^^^3.
About Ackermann numbers, I use this definition:
http://mathworld.wolfram.com/AckermannNumber.html
(Same series like yours.)
The value of 3^^4 :
3^^4 = 3^3^3^3 = 3^7,625,597,484,987 =
approx. 1.258 * 10^3,638,334,640,024 (over three
trillion digits long). See:
http://en.wikipedia.org/wiki/Tetration
Another interesting article is "Large Numbers" (6
pages) at:
http://home.earthlink.net/~mrob/pub/math/largenum.html
The author starts with, "Large numbers have interested
me almost all my life."
I better let the mathematicians calculate the value of
3^^^3. Probably, I can live with formula-free number
names. See:
http://www.unc.edu/~rowlett/units/large.html
Bye,
Suyono
prokofiev2006 wrote:
Thank you for the correction. Yes, you are right.
That article ("The Challenge of Large Number") was in
Scientific American. I didn't notice that when it says
Ackermann numbers (at the end of article); it means
DIFFERENT Ackermann numbers. It's 3^^4,
not 3^^^3.
About Ackermann numbers, I use this definition:
http://mathworld.wolfram.com/AckermannNumber.html
(Same series like yours.)
The value of 3^^4 :
3^^4 = 3^3^3^3 = 3^7,625,597,484,987 =
approx. 1.258 * 10^3,638,334,640,024 (over three
trillion digits long). See:
http://en.wikipedia.org/wiki/Tetration
Another interesting article is "Large Numbers" (6
pages) at:
http://home.earthlink.net/~mrob/pub/math/largenum.html
The author starts with, "Large numbers have interested
me almost all my life."
I better let the mathematicians calculate the value of
3^^^3. Probably, I can live with formula-free number
names. See:
http://www.unc.edu/~rowlett/units/large.html
Bye,
Suyono
prokofiev2006 wrote:
>
> 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
>