View Full Version : p-adic numbers

2012-Aug-09, 02:54 PM
What does 'adic' mean in maths?

Are there any good, beginner sites that explain p-adic numbers?

2012-Aug-09, 03:02 PM
Here's the Wiki page, it's not very "beginner", but it links to several other pages that may be a little easier to understand.


Here is another good explanation:


2012-Aug-09, 04:42 PM
The adic is a suffix described here (http://en.wiktionary.org/wiki/-adic). The p means that you are dealing with positive numbers. I had previously thought that the p meant "prime", but the wikipedia article states otherwise ( and we all know that wikipedia is always right).

2012-Aug-09, 04:46 PM
What does 'adic' mean in maths?

You're referring to p-adic numbers, of course, but the suffix itself is kinda ordinary. Dictionary.com has the definition for -ad:

1.*a suffix occurring in loanwords from Greek denoting a group or unit comprising a certain number, sometimes of years: dyad, triad
We also see it in "monad", and mathematics just generalizes it to "p-ad" where p stands for any number, like 4-ad or 7-ad.

The -ic is familiar too, again from dictionary.com:

1.*a suffix forming adjectives from other parts of speech, occurring originally in Greek and Latin loanwords: metallic, poetic, archaic, public

We have the words "triadic" and "dyadic", and similarily, we have 4-adic numbers and 7-adic numbers.

Are there any good, beginner sites that explain p-adic numbers?
Those wiki pages are pretty good, but as you can see, it's not really a simple concept.