It’s a ludicrously large number in Knuth’s up-arrow notation used in some posts as an example of a number which is finite, but large enough to ludicrously surpass reasonable finite numbers like the size of the universe, or the number of possible states of a volume the size of the Solar System, or whatever.
But why is “3” chosen rather than another single-digit integer? I can see why 0 or 1 would not be chosen, obviously, and 2 could confuse people by appearing non-arbitrary due to the role of binary in computer science. Is 3 simply the first viable positive integer that came along?
2^^^...2 is 4 for any number of up-arrows. 3^^^3 is the first, simplest Knuth number (a three, three up-arrows, and a three) to give stupendously large values, far outstripping 2^^^4 or 4^^^2.
It’s a ludicrously large number in Knuth’s up-arrow notation used in some posts as an example of a number which is finite, but large enough to ludicrously surpass reasonable finite numbers like the size of the universe, or the number of possible states of a volume the size of the Solar System, or whatever.
But why is “3” chosen rather than another single-digit integer? I can see why 0 or 1 would not be chosen, obviously, and 2 could confuse people by appearing non-arbitrary due to the role of binary in computer science. Is 3 simply the first viable positive integer that came along?
2^^^...2 is 4 for any number of up-arrows. 3^^^3 is the first, simplest Knuth number (a three, three up-arrows, and a three) to give stupendously large values, far outstripping 2^^^4 or 4^^^2.
Ah ha, upon wiki’ing, I was bungling how up-arrow notation worked. Thank you!