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You are not logged in. #1 20070221 01:37:41
Factorials, Hyperfactorials and SuperfactorialsThe factorial notation must be familiar to most of you. Thus, H(1) = 1, H(2) = 4, H(3) = 108 and so on. Finally, the Superfactorial. Clifford Pickover in his 1995 book Keys to Infinity defined the superfactorial of n as When expressed in Knuth's uparrow notation. n$=n!^^n! For example, The function grows very rapidly and as n increases, the tower of powers increases at a very quick rate. 100$ would have more powers in the tower than a Googol! And 1000$ would have more powers in the tower than . These are extremely large numbers, and absolutely useless to a common man! That is because a person may never encounter a number greater than for most of his/her life, and certainly never ever think of anything near unless he's/she's a mathematician! Character is who you are when no one is looking. #2 20070221 03:58:25
Re: Factorials, Hyperfactorials and SuperfactorialsIs the hyperfactorial meant to be: #3 20070221 15:09:46
Re: Factorials, Hyperfactorials and SuperfactorialsYes, you are correct, Patrick! Character is who you are when no one is looking. #4 20070221 18:12:02
Re: Factorials, Hyperfactorials and SuperfactorialsIn Knuth's upper arrow notation, how many powers do you raise n to? #5 20070221 18:45:38
Re: Factorials, Hyperfactorials and Superfactorials
Oh well, I guess I'm turning blind.. Thanks for sharing the knowledge though Had never heard of hyperfactorials before! #6 20070221 19:16:43
Re: Factorials, Hyperfactorials and Superfactorials
means raise a to itself n1 times. For example, Then basically there is a "tower" of n a's. I can post more on this notation once I figure out how to make the LaTeX work here. (does someone know how to do underbraces in this forum? I can't see you get it to work) #7 20070222 08:15:09
Re: Factorials, Hyperfactorials and Superfactorials
Last edited by Patrick (20070222 08:15:31) 