“Goodstein's Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Goodstein's Theorem

释义

Goodstein's Theorem

For all , there exists a such that the th term of the Goodstein Sequence . In other words, everyGoodstein Sequence converges to 0.

The secret underlying Goodstein's theorem is that the Hereditary Representation of in base mimics anordinal notation for ordinals less than some number. For such ordinals, the base bumping operation leaves the ordinal fixedwhereas the subtraction of one decreases the ordinal. But these ordinals are well-ordered, and this allows us to concludethat a Goodstein sequence eventually converges to zero.

Goodstein's theorem cannot be proved in Peano Arithmetic(i.e., formal Number Theory).

See also Natural Independence Phenomenon, Peano Arithmetic

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。