A simple finitary proof of Goodstein's Theorem
General Mathematics
2011-04-26 v2
Abstract
We assumed that, for every natural number k, there is a natural number u such that the (k-1)th term of G(u) is k^k, and that G(u) terminates finitely. It immediately follows that every Goodstein Sequence G(m) over the natural numbers must terminate finitely. The assumption is easily seen to be false since there is no m such that the third term of g(m) is 4^4.
Keywords
Cite
@article{arxiv.1104.4111,
title = {A simple finitary proof of Goodstein's Theorem},
author = {Bhupinder Singh Anand},
journal= {arXiv preprint arXiv:1104.4111},
year = {2011}
}
Comments
This paper has been withdrawn by the author due to an elementary flaw in the argument of Theorem 1