p-adic ordinal

noun1

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.