What does p-adic number mean?

Definitions for p-adic number

Here are all the possible meanings and translations of the word p-adic number.


  1. p-adic number(Noun)

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


  1. p-adic number

    In mathematics the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, p-adic numbers have the interesting property that they are said to be close when their difference is divisible by a high power of p – the higher the power the closer they are. This property enables p-adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles. p-adic numbers were first described by Kurt Hensel in 1897, though with hindsight some of Kummer's earlier work can be interpreted as implicitly using p-adic numbers. The p-adic numbers were motivated primarily by an attempt to bring the ideas and techniques of power series methods into number theory. Their influence now extends far beyond this. For example, the field of p-adic analysis essentially provides an alternative form of calculus.


  1. Chaldean Numerology

    The numerical value of p-adic number in Chaldean Numerology is: 5

  2. Pythagorean Numerology

    The numerical value of p-adic number in Pythagorean Numerology is: 7

Images & Illustrations of p-adic number


Find a translation for the p-adic number definition in other languages:

Select another language:

Discuss these p-adic number definitions with the community:

Word of the Day

Would you like us to send you a FREE new word definition delivered to your inbox daily?

Please enter your email address:     


Use the citation below to add this definition to your bibliography:


"p-adic number." Definitions.net. STANDS4 LLC, 2017. Web. 25 May 2017. <http://www.definitions.net/definition/p-adic number>.

Are we missing a good definition for p-adic number? Don't keep it to yourself...

Nearby & related entries:

Alternative searches for p-adic number:

Thanks for your vote! We truly appreciate your support.