*p*-adic ordinal

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

** p-adic ordinal** (

*plural*

**p-adic ordinals**)

- (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*p*^{r}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.

- Notice the resemblance between the

#### Usage notes[edit]

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

#### Related terms[edit]

### References[edit]

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