p-adic ordinal

English

Noun

p-adic ordinal (plural p-adic ordinals)

1. (number theory) A function of rational numbers, with prime number p as parameter, which is defined for some non-zero integer x as the largest integer r such that p^r divides x; is defined for some non-zero rational number a/b as the p-adic ordinal of a minus the p-adic ordinal of b; and is defined for 0 as infinity.

   Notice the resemblance between the p-adic ordinal and the base-p logarithm.

Usage notes

• The p-adic ordinal of rational number x can be denoted as ${\mbox{ord}}_{p}\,x$.

Related terms

• p-adic norm