Graham’s number is an immense number that arose as an upper bound for a problem in Ramsey theory. It is vastly larger than numbers such as Skewes’s number and Moser’s number, which are themselves much larger than a googolplex. Graham’s number is so enormous that the observable universe would be far too small to contain its ordinary decimal representation, even if each digit occupied only one Planck volume. The number of digits in Graham’s number is itself so enormous that even that number could not be physically represented in the observable universe. The same applies repeatedly to the number of digits of that number, and so on. Despite its incredible size, Graham’s number can be precisely defined using a recursive formula and Knuth’s up-arrow notation. It is written as g_64, where: g_1 = 3 ↑↑↑↑ 3 and for n ≥ 2: g_n = 3 ↑^(g_(n-1)) 3 Although Graham’s number can never realistically be written out in full, individual digits can be calculated using algorithms. Its last ten digits are 2464195387. Graham’s number was named after mathematician Ronald Graham. Graham discussed the number with science writer Martin Gardner while explaining an upper bound for a problem he was studying. In 1977, Gardner described it in Scientific American, bringing the number to a much wider audience. At the time, it was the largest specific positive integer ever used in a published mathematical proof. It was later included in the 1980 Guinness Book of World Records, which increased its popularity. Graham’s number is still unimaginably large, but it is not the largest number used in serious mathematics. Numbers such as TREE(3), associated with results related to Kruskal’s theorem, are vastly larger. Smaller upper bounds for the Ramsey theory problem that originally led to Graham’s number have also since been found. Graham’s number is therefore famous less because it is the absolute largest possible number and more because it provides a precise example of how mathematics can define numbers far beyond anything that could ever be physically written down. #humanity #hero #alightmotion #edit #antitccedit - @darnelloo9487_