p-adic ordinal

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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 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. [1]
    Notice the resemblance between the p-adic ordinal and the base-p logarithm.

Usage notes[edit]

  • The p-adic ordinal of rational number x can be denoted as .

Related terms[edit]


  1. ^ 2011, Andrew Baker, An Introduction to p-adic Numbers and p-adic Analysis, Definition 2.3