# Definitions for goodstein's theoremgood·stein's the·o·rem

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1. 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. Kirby & Paris 1982 showed that it is unprovable in Peano arithmetic. This was the third "natural" example of a true statement that is unprovable in Peano arithmetic. Earlier statements of this type had either been, except for Gentzen, extremely complicated, ad-hoc constructions or concerned metamathematics or combinatorial results. Laurie Kirby and Jeff Paris gave an interpretation of the Goodstein's theorem as a hydra game: the "Hydra" is a rooted tree, and a move consists of cutting off one of its "heads", to which the hydra responds by growing a finite number of new heads according to certain rules. The Kirby–Paris interpretation of the theorem says that the Hydra will eventually be killed, regardless of the strategy that Hercules uses to chop off its heads, though this may take a very, very long time.

### Numerology

1. Chaldean Numerology

The numerical value of goodstein's theorem in Chaldean Numerology is: 2

2. Pythagorean Numerology

The numerical value of goodstein's theorem in Pythagorean Numerology is: 4

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"goodstein's theorem." Definitions.net. STANDS4 LLC, 2022. Web. 21 Jan. 2022. <https://www.definitions.net/definition/goodstein%27s+theorem>.

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