p-adic ultrametric

英語（米国） (en-US) 英語（イギリス） (en-GB)

名詞

(number theory) The ultrametric with prime number p as parameter defined as d_p(x,y)=|x-y|ₚ; i.e., such that the distance between two rational numbers is equal to the p-adic absolute value of the difference between those two numbers.

日本語の意味

「p-adic ultrametric」とは、数論の分野で、素数pをパラメーターとする超距離（ultrametric）を意味し、2つの有理数x, y間の距離を、差x - yのp進絶対値 |x-y|ₚ により定義する。

英語の意味

(number theory) The ultrametric with prime number p as parameter defined as d_p(x,y)=|x-y|ₚ; i.e., such that the distance between two rational numbers is equal to the p-adic absolute value of the difference between those two numbers.

このボタンはなに？

The p-adic ultrametric d_p(x,y)=|x-y|_p reveals surprising topological properties, such as total disconnectedness and the strong triangle inequality.

素数pのp進絶対値によって定義される超距離 d_p(x,y)=|x-y|_p は、位相的に全く連結でないことや強い三角不等式を満たすなどの驚くべき性質を示す。

詳細

意味（1）

(number theory) The ultrametric with prime number p as parameter defined as d_p(x,y)=|x-y|ₚ; i.e., such that the distance between two rational numbers is equal to the p-adic absolute value of the difference between those two numbers.

p-adic ultrametrics （ plural ）