infinite descent

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

不可算名詞

(mathematics) A method of proof by contradiction that is used to prove that a statement must be false for all positive integers. By showing that if it is true for one integer, it must be true for a smaller integer, an infinite number of solutions are found and a contradiction is eventually reached.

日本語の意味

数学において、背理法を用いてある命題が真であると仮定した場合、ある正の整数で成立すれば必ずより小さい正の整数で成立するという連鎖を導き、結果として無限に小さい正の整数が存在する矛盾を示す手法。これにより、その命題が偽であることを証明する方法。

英語の意味

(mathematics) A method of proof by contradiction that is used to prove that a statement must be false for all positive integers. By showing that if it is true for one integer, it must be true for a smaller integer, an infinite number of solutions are found and a contradiction is eventually reached.

このボタンはなに？

The number theorist applied infinite descent to show that no positive integer solution exists.

その数論家は、正の整数解が存在しないことを示すために無限降下法を用いた。

詳細

意味（1）

(mathematics) A method of proof by contradiction that is used to prove that a statement must be false for all positive integers. By showing that if it is true for one integer, it must be true for a smaller integer, an infinite number of solutions are found and a contradiction is eventually reached.