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David Metzler's series "Ridiculously Huge Numbers"[1] is a good introduction to this. It goes rather well beyond puny little integers like Graham's number. Loa

David Metzler's series "Ridiculously Huge Numbers"[1] is a good introduction to this. It goes rather well beyond puny little integers like Graham's number. Loader's number has already been mentioned here, but I don't see any mention of the Busy Beaver function[2]. BB(n) is the maximum number of 1s that can be written of a 2-color, n-state halting Turing machine starting from a blank tape and counted after the machine halts. This is of course uncomputable, and grows very quickly. Rayo's function (Rayo(n) = the smallest natural number greater than all natural numbers that can be uniquely identified by a first order set theory expression of at most n symbols) grows even faster, but that requires a non-recursively enumerable set theory or the use of non-provable functions. [1] https://www.youtube.com/watch?v=QXliQvd1vW0&list=PL3A50BB9C34AB36B3 https://www.youtube.com/watch?v=QXliQvd1vW0&list=PL3A50BB9C3... [2] http://googology.wikia.com/wiki/Busy_Beaver http://googology.wikia.com/wiki/Busy_Beaver

speakeron 9y ago
> David Metzler's series "Ridiculously Huge Numbers"[1] is a good introduction to this. It goes rather well beyond puny little integers like Graham's number. Yes, David Metzler's series is great and, I would say, essential viewing if your interest in large numbers is piqued. While he doesn't go through some of the big numbers talked about her (TREE(3), SCG(13), etc), he gives an excellent explanation of the fast-growing hierarchy. This is really the closest thing we have to a 'standardized' way of comparing the sizes of very large numbers. I would also recommend Giroux Studios' 'Extremely Large Numbers'[1], which takes a similar style to Metzler's videos and goes further with the fast-growing hierarchy. (Does something called 'infinite collapsing functions' sound interesting...?) [1] https://www.youtube.com/watch?v=vq2BxAJZ4Tc&list=PLUZ0A4xAf7nkaYHtnqVDbHnrXzVAOxYYC https://www.youtube.com/watch?v=vq2BxAJZ4Tc&list=PLUZ0A4xAf7...
- SAI_Peregrinus 9y ago
  Metzler's series got expanded a while back, he does have some sections on TREE (though not on SCG, SSCG, etc). IIRC there's a brief bit about ordinal collapsing functions as well, but not very detailed.
  - asah 9y ago
    Let me propose YOUTUBE(n) which represents the number of YouTube videos about the mathematics of large numbers.

speakeron 9y ago

> David Metzler's series "Ridiculously Huge Numbers"[1] is a good introduction to this. It goes rather well beyond puny little integers like Graham's number. Yes, David Metzler's series is great and, I would say, essential viewing if your interest in large numbers is piqued. While he doesn't go through some of the big numbers talked about her (TREE(3), SCG(13), etc), he gives an excellent explanation of the fast-growing hierarchy. This is really the closest thing we have to a 'standardized' way of comparing the sizes of very large numbers. I would also recommend Giroux Studios' 'Extremely Large Numbers'[1], which takes a similar style to Metzler's videos and goes further with the fast-growing hierarchy. (Does something called 'infinite collapsing functions' sound interesting...?) [1] https://www.youtube.com/watch?v=vq2BxAJZ4Tc&list=PLUZ0A4xAf7nkaYHtnqVDbHnrXzVAOxYYC https://www.youtube.com/watch?v=vq2BxAJZ4Tc&list=PLUZ0A4xAf7...

SAI_Peregrinus 9y ago
Metzler's series got expanded a while back, he does have some sections on TREE (though not on SCG, SSCG, etc). IIRC there's a brief bit about ordinal collapsing functions as well, but not very detailed.
- asah 9y ago
  Let me propose YOUTUBE(n) which represents the number of YouTube videos about the mathematics of large numbers.