3 ms·
Double exponential growth is crazy fast, but some problem grow much faster and follow the hyperoperation sequence growth rate. Knuth wrote a fun paper in Scienc
by todd8 7y ago
Double exponential growth is crazy fast, but some problem grow much faster and follow the hyperoperation sequence growth rate. Knuth wrote a fun paper in Science in 1976 [1]. (Easy & interesting but sadly my link is to a paywall.)
That was the first place I saw his arrow notation to describe some of these numbers.
5↑3 = 5*(5*5)
5↑↑3 = 5↑(5↑5)
5↑↑↑3 = 5↑↑(5↑↑5)
5↑↑↑↑3 = 5(↑^4)3
These numbers get BIG, the up arrow notation can express the Ackermann function.
[1] https://science.sciencemag.org/content/194/4271/1235 https://science.sciencemag.org/content/194/4271/1235