Goodstein's Theorem

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence eventually terminates at 0. Laurence Kirby and Jeff Paris showed in 1982 that Goodstein's theorem is unprovable in Peano arithmetic, making it the third known example of a true statement about natural numbers that Peano arithmetic cannot prove, after Godel's incompleteness theorem and Gerhard Gentzen's 1943 proof of the unprovability of epsilon-zero induction; the Paris-Harrington theorem gave another example. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/