definition (N$\times$N)$\Rightarrow$N
(n,m)=n^n^...^n (the number of n is m)
Does this operation has a name? Is there a book studying the nature of this operation?
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“definition $N\times N \to N$ “, which is what I assume was meant, doesn’t make sense here. – Adam Rubinson Feb 25 '22 at 15:46
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3Tetration, I believe. One of the hyperoperations – FShrike Feb 25 '22 at 15:46
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3Yes, tetration: https://en.wikipedia.org/wiki/Tetration – Jaap Scherphuis Feb 25 '22 at 15:52
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This can be generalized to Knuth's up-arrow notation. A power tower with $b$ copies of $a$ is usually written as "$a\uparrow \uparrow b$". The main purpose of this function is to produce ridiculous large numbers (in most cases integers although $a$ can be any positive real number) – Peter Feb 25 '22 at 16:54