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What is a p-adic ordinal?

What is a p-adic ordinal? Here are some definitions.

Noun
  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 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.
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