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Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number , both of which are in turn much larger than a googolplex .
Thus the "order of magnitude" of a number (on a larger scale than usually meant), can be characterized by the number of times (n) one has to take the to get a number between 1 and 10. Thus, the number is between 10 ↑ ↑ n {\displaystyle 10\uparrow \uparrow n} and 10 ↑ ↑ ( n + 1 ) {\displaystyle 10\uparrow \uparrow (n+1)} .
Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex. [8] [9]
In computability theory, computational complexity theory and proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg-Wainer hierarchy) [1] is an ordinal-indexed family of rapidly increasing functions f α: N → N (where N is the set of natural numbers {0, 1, ...}, and α ranges up to some large countable ordinal).
At the same time that he suggested "googol" he gave a name for a still larger number: "googolplex". A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired.
Mathematics:, a number in the googol family called a googolplexplex, googolplexian, or googolduplex. 1 followed by a googolplex zeros, or 10 googolplex Cosmology: The uppermost estimate to the size of the entire universe is approximately 10 10 10 122 {\displaystyle 10^{10^{10^{122}}}} times that of the observable universe .
Graham's number has 64 of the up arrows, so it's much more than what a brain can comprehend without just thinking of infinity. 98.223.56.77 02:14, 22 September 2008 (UTC) Graham's number has many, many, many more than 64 up arrows. g 1 has 4 up arrows. g 2 has g 1 up arrows.
Upper bounds on Skewes's number Year near x # of complex zeros used by 2000: 1.39822 × 10 316: 10 6: Bays and Hudson 2010: 1.39801 × 10 316: 10 7: Chao and Plymen 2010: 1.397166 × 10 316: 2.2 × 10 7: Saouter and Demichel 2011: 1.397162 × 10 316: 2.0 × 10 11: Stoll and Demichel