# p-adic ordinal

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## English

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### 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 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

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

### References

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