### Definition of P-adic absolute value

1. Noun. (number theory field theory) a norm for the rational numbers, with some prime number ''p'' as parameter, such that any rational number of the form $p^k \Big\left(\left\{a\over b\right\}\Big\right)$ — where ''a'', ''b'', and ''p'' are coprime and ''a'', ''b'', and ''k'' are integers — is mapped to the rational number $p^\left\{-k\right\}$, and 0 is mapped to 0. (''Note:'' any rational number, except 0, can be reduced to such a form.) '''2008''', Jacqui Ramagge, [ Unreal Numbers: The story of ''p''-adic numbers] (PDF file) ¹

¹ Source: wiktionary.com

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### Lexicographical Neighbors of P-adic Absolute Value

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