Googolplex: Difference between revisions

Revision as of 02:55, 29 May 2009

Revision as of 22:19, 29 May 2009

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Found to be even bigger was the "googol megaplex", as defined by Alan Agon (University of New South Wales, Sydney Australia, 7 May 2009), also using Knuth's up-arrow notation as <math>Ghp \uparrow\uparrow Ghp</math>, where "Ghp" is a googol hyperplex.{{Fact|date=January 2009}}

Found to be even bigger was the "googol gigaplex"as defined by Bill Hall (England 29 May 2009), using Knuth's up-arrow notation as:

GMeP ↑↑ GMeP, where "GMeP" is a googol megaplex.

A [[Turing machine]] formalizes the notion of a procedure or ''[[algorithm]]'', and a [[busy beaver]] is the Turing machine of size ''n'' that can write down the biggest possible number.<ref>http://mathworld.wolfram.com/BusyBeaver.html</ref> The bigger ''n'' is, the more complex the busy beaver, hence the bigger the number it can write down. For {{nowrap|1= ''n'' = 1, 2, 3, 4 and 5}} the [[Busy beaver#Exact values and lower bounds for some S(n, m) and Σ(n, m)|numbers expressible]] are not huge, but research as of 2008 shows that for {{nowrap|1= ''n'' = 6}} the busy beaver can write down a number at least as big as {{nowrap|4.640 × 10}}¹⁴³⁹.<ref>[http://www.drb.insel.de/~heiner/BB/index.html Marxen, Heiner, "Busy Beaver"], 27 Oct., 2008.</ref>