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 Hoping Frank can help me with more maths... (Read 4390 times)
abyssoft
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Hoping Frank can help me with more maths...
09/26/10 at 15:29:51

given the following in Knuth's notation

 [(10!↑↑1083)!↑↑1047] (10!↑↑1083)

What is the simplification of the above number in scientific notation?
I am imagining that this is both difficult to do and will result in an extremely large exponent.

I understand the following about this number... (10!↑↑1083) can be represented as the following series
 10! ⋰ 1083 - 3 times 10! 10!

I found this listed in a scifi book as a reference to the amount of time in years to equal the fullness of time. and I'm just curious as to what it equates to.
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 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Hoping Frank can help me with more maths... Reply #1 - 09/26/10 at 22:59:12   really big number Abby !     If 10 fac= 3628800 and you raise it 80 times with this exponent , its the same as to raise it  once to the exponent 80*3628800= 290304000   So one gets : (3628800)^(290304000) Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Hoping Frank can help me with more maths... Reply #2 - 09/27/10 at 08:11:05   I'm having difficulty with this concept.       2^2 2^2^2^   You say would be the equivalent of 2^(2*4) which would be 256 however if you work it out by step you get         4 2^2^2^   2^2^16   2^65536 which is a lot more then 256 So what am I either missing or misconceiving? Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Hoping Frank can help me with more maths... Reply #3 - 09/27/10 at 09:46:25   Quote from frankuitaalst on 09/26/10 at 22:59:12:really big number Abby ! If 10 fac= 3628800 and you raise it 80 times with this exponent , its the same as to raise it  once to the exponent 80*3628800= 290304000 So one gets : (3628800)^(290304000)   Sorry , I was to quick   ; youre right   It should be : (3628800)^((3628000)^80) which is in fact ...unexpressible ... Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Hoping Frank can help me with more maths... Reply #4 - 10/01/10 at 08:57:06   I've almost been able to get my computer to represent 10!^10! let's just say it's a really big number, I've got 2 more calculation rounds to complete before it's done and it's already over 2 million digits in length I Figure the last 2 round will be completed by weekends end. I am now very much believing that given current technology, storage and processing power, and the progress of said technologies it will be quite some time until it can be expressed.   I did figure a way to calculate faster while I was typing this message, and for those curious enough about it I'll attached a zip of the text output in a following message. trailing zeros will have been striped and be presented in scientific notation. Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Hoping Frank can help me with more maths... Reply #5 - 10/02/10 at 12:53:30   Calculation complete and so attached is 10! ^ 10! Back to top IP Logged
 frankuitaalst Ultimate Member Great site Posts: 1508 Gender: Re: Hoping Frank can help me with more maths... Reply #6 - 10/02/10 at 13:58:50   waw !! how did you do this ? Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Hoping Frank can help me with more maths... Reply #7 - 10/02/10 at 22:21:25   I created a small .Net Window Application that utilized C# BigInt found at http://www.emilstefanov.net/Projects/GnuMpDotNet/ which gives access to integers of arbitrary length and several math functions and operations. Back to top IP Logged
 abyssoft YaBB Administrator I love YaBB 1G - SP1! Posts: 302 Re: Hoping Frank can help me with more maths... Reply #8 - 10/02/10 at 22:33:11   given the size of just 10! ^ 10!     10!^^1083 is quite unfathomably large and (10!^^1083!)^^1047 is beyond mind-blowingly large.     (10!^^1083) ^ [(10!^^1083!)^^1047] Is beyond all possible comprehension as this point in human evolution. Back to top IP Logged
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