What does "adic" mean?

Question

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.

I always thought it was a suffix -adic not a word. As for what it means exactly, I'm not sure. — Dan, Dec 04 '14 at 13:43
@Dan This does not appear in the dictionary I mentioned, neither as a word, nor as a suffix. — sunkist, Dec 04 '14 at 13:52
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. — apnorton, Dec 04 '14 at 14:09
@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. — sunkist, Dec 04 '14 at 14:31
I always assumed, like user8268, that it was by analogy with dyadic, triadic, tetradic, etc. Make the root number a variable, $p$, and there you go. — , Dec 04 '14 at 16:42

score 6 · Answer 1 · edited Dec 04 '14 at 16:04

6

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)

edited Dec 04 '14 at 16:04

apnorton

17,706

answered Dec 04 '14 at 14:56

TonyK

64,559

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. – AlexR Dec 04 '14 at 15:00
@AlexR: Now I can't access it either! Strange -- it worked when I posted it. – TonyK Dec 04 '14 at 15:06
@anorton: Thanks for the edit! – TonyK Dec 04 '14 at 17:14
1

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." – Cheerful Parsnip Dec 04 '14 at 20:13
The third definition is also seen in programming, especially for variadic function – Nayuki Mar 02 '16 at 03:44

What does "adic" mean?

1 Answers1