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Graham's Number basics PDF Print E-mail
Written by Administrator   
Sunday, 11 December 2011 19:21

As I'm called Graham I felt this was kinda cool. May be you do too.

 

Googol = 10100 = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
The number of particles in the universe is less than a googol.

Googolplex = 10googol = 1010100 (= 10^10^100).

100 factorial = 100! = 1 x 2 x 3 x ... x 100 = 9.3326... x 10157 =
93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,
895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,
185,210,916,864,000,000,000,000,000,000,000,000.
Can you figure out why 100 factorial ends with 24 zeros?

Skewe's number: In 1933, Stanley Skewes used the number 10101034 (= 10^10^10^34) in a proof involving prime numbers. G. H. Hardy said it was "the largest number which has ever served any definite purpose in mathematics".

Graham's number: In 1971, Ronald Graham used a much larger number in a proof involving combinatorics. The number is so large that it takes a page just to describe how to write the number. Martin Gardner called it "the largest number ever used in a serious mathematical proof". The Guiness Book of World Records listed it as the largest useful number.

 

Graham's number is truly amazing, so big that it's easy to underestimate it. Gerhard Paseman has seriously underestimated how big Graham's number is in terms of the Ackermann function. A(m,n)=2?(m-2)(n+3)-3. So the first step of the Graham's function, 3????3 = g1, is very roughly A(6,6). The second step g2 is roughly A(g1,g1) and the actual Graham's number, g64, is roughly A(g63,g63). That's how big Graham's number is.

The question marks in the last equation should have been arrows pointing up to denote 'to the power of' but couldn't get them to work in HTML.

Last Updated on Sunday, 11 December 2011 19:46
 

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