The word "adic" is often seen in books of algebra and number theory. I don't know what does this word mean, so I look it up in a dictionary, called Oxford Dictionary of English. But it does not appear there.

So what does this word mean just as a word, and why is it used in defining the mathematical concepts?

I am sorry if this question seems weird. English is not mother language.

Thanks for any help.

  • $\begingroup$ I always thought it was a suffix -adic not a word. As for what it means exactly, I'm not sure. $\endgroup$ – Dan Dec 4 '14 at 13:43
  • $\begingroup$ @Dan This does not appear in the dictionary I mentioned, neither as a word, nor as a suffix. $\endgroup$ – sunkist Dec 4 '14 at 13:52
  • 2
    $\begingroup$ might be coming from dyad, triad (wilde guess) $\endgroup$ – user8268 Dec 4 '14 at 13:54
  • $\begingroup$ It might have some German ties, as that seems to be (according to MathWorld) the language used by the first person to "come up" with the concept of p-adic numbers. $\endgroup$ – apnorton Dec 4 '14 at 14:09
  • $\begingroup$ @anorton Thank you. I guess if this is the case, then "p-adic" might be created by someone who wanted to translate "p-adische" into English. $\endgroup$ – sunkist Dec 4 '14 at 14:31

The OED Online has an entry for -adic.

The first definition relates to chemistry, while the second and third definitions relate to mathematics:

Second definition:

Math. With preceding symbol or numeral (esp. the generalized symbol p, denoting a prime number), forming adjectives designating numbers expressible as a sequence of digits in the base represented by the symbol (or as a power series in this quantity).

Third definition:

Chiefly Math. and Logic. With preceding symbol (usu. n), forming adjectives designating a function, operator, relation, etc., having the number of arguments represented by the given symbol. Cf. -ary suffix1 Additions.

(Accessed 12/4/14, 11:03am)

  • $\begingroup$ I don't have access to the link (it redirects to the homepage). You should copy the excerpt as a quote to make it self-contained. But who am I to complain. $\endgroup$ – AlexR Dec 4 '14 at 15:00
  • $\begingroup$ @AlexR: Now I can't access it either! Strange -- it worked when I posted it. $\endgroup$ – TonyK Dec 4 '14 at 15:06
  • $\begingroup$ @anorton: Thanks for the edit! $\endgroup$ – TonyK Dec 4 '14 at 17:14
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    $\begingroup$ As listed in the OED, the etymology is from the two suffixes -ad and -ic, where the suffix -ad means "forming collective numerals" and is the same suffix that appears in "olympiad." $\endgroup$ – Cheerful Parsnip Dec 4 '14 at 20:13
  • $\begingroup$ The third definition is also seen in programming, especially for variadic function $\endgroup$ – Nayuki Mar 2 '16 at 3:44

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