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Bookmark or Share- GOODSTEIN’S THEOREM, , AND UNPROVABILITY - University of PennsylvaniaGOODSTEIN’S THEOREM, 0, AND UNPROVABILITY 5 Tocompareωω2#ωω toωω2#ω8,wecomparethelistofexponents: the list ω2 ≥ω1 from the first ordinal with the list ω2 ≥8 from the second ordinal; since the first component of the lists are the same, we go to the secondcomponent. Sinceω1 ≥8,ωω2#ωω islarger. For one more example, compare ωω2#ωω#ω8 to ωω2#ωω.
- Goodstein Sequence -- from Wolfram MathWorldStarting this procedure at an integer gives the Goodstein sequence . Amazingly, despite the apparent rapid increase in the terms of the sequence, Goodstein's theorem states that is 0 for any and any sufficiently large .
- 古德斯坦定理 - 百度百科古德斯坦定理是由鲁宾·古德斯坦提出的一条关于 自然数 的命题，即所有古德斯坦序列最终均结束于0。 古德斯坦本人用集合论方法证明了这个定理，科比和 帕里斯 则在 1982年 证明了该命题在 皮亚诺公理系统 内是不可证的。 问题陈述继承n进制表示古德斯坦序列是由一种称为“继承n进制表示”的 ...
- Goodstein's theorem - WikipediaIn mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which states that every Goodstein sequence (as defined below) eventually terminates at 0.
- Reuben Goodstein - WikipediaReuben Louis Goodstein (15 December 1912 – 8 March 1985) was an English mathematician with an interest in the philosophy and teaching of mathematics. [3]
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