Mathematics and Applied Mathematics
June 4, 2020
expofactorial numbers, n-expofactorial numbers, hypothesis of the actual infinity
This paper defines, in precise arithmetic terms, non-computable natural numbers. Not even the approximate number of their ciphers can be computed. We can define them, but nothing can be known on their precise sequence of ciphers. Obviously, these numbers are absolutely useless, but they illustrate how large a finite natural number can really be. And, most importantly, they illustrate the futility of the transfinite numbers, whether cardinals or ordinals.