p-adic ordinal

Noun

 * 1)  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 pr 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