# P-adic-number Definition

noun

(mathematics) An element of a completion of the field of rational numbers which has a *p*-adic ultrametric as its metric.

The expansion (21)2121p is equal to the rational p-adic number .

In the set of

**3-adic numbers**, the closed ball of radius 1/3 "centered" at 1, call it B, is the set . This closed ball partitions into exactly three smaller closed balls of radius 1/9: , and . Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner.Likewise, going upwards in the hierarchy, B is part of the closed ball of radius 1 centered at 1, namely, the set of integers. Two other closed balls of radius 1 are "centered" at 1/3 and 2/3, and all three closed balls of radius 1 form a closed ball of radius 3, which is one out of three closed balls forming a closed ball of radius 9, and so on.Wiktionary

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## Other Word Forms of P-adic-number

### Noun

Singular:

p-adic-number
Plural:

p-adic numbers