# Talk:Arity

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## Unwarranted domain-specific language

Consider the following:

Also, in non-functional programming, a function without arguments can be meaningful and not necessarily constant (due to side effects).

Technically, "pure" should replace "functional", but programming is impure by default (pure programming is a special case of general programming). — Preceding unsigned comment added by 173.176.165.23 (talk) 08:03, 29 April 2012 (UTC)

## What's up with the list of adjectives?

The list of adjectives "unary", "binary", "ternary", ... is informative but it should link to the wiktionary, not the wikipedia. I'll do that asap. Having "denary" point to Decimal is rather confusing...

Perhaps the wiktionary is the best home for the full list? PhS 12:01, 1 September 2005 (UTC)

Um, it's been a few weeks... I think I'll shift it around myself. Melchoir 23:44, 29 September 2005 (UTC)

## Rarity of higher arities

Actually, it's arities above 2 that are rare. Further, the alleged reason seems invalid to me. The fact that one could formally represent any n-ary operation with n > 2 as the composition of binary operations by using a cute trick is quite separate from the fact that we relatively rarely have a use for such operations in mathematics. I've removed most of this statement but I preserve it here in case anyone can find a good justification, or some use for it:

Arities greater than 4 are seldom encountered in mathematics and computer science. This fact has a mathematical justification. Burris and Sankappanavar (1981: Ex. IV.7.8) attribute to Sierpinski a theorem to the effect that any finitary operation on a finite set can be expressed as the composition of binary operations.

Zaslav 07:55, 25 June 2006 (UTC), Zaslav 18:31, 25 June 2006 (UTC)

Actually arities above 2 aren't very rare. Take Integration for example; An operation on a given function (operand), starting value (operand), ending value (operand). Another example: Summation (for the same reason, function, start, end). Another Example (capital PI notation for products of sequences, same as before). Of course, one may argue that one is really performing the integration over an interval (just one operand) or over an area/volume/etc. as just one operand, and it is just convention to define that volume with a list of various values.
[visitor: Litchfield 11:45 a.m. MDT, 3 Feb. 2010 —Preceding unsigned comment added by 155.97.18.26 (talk) 18:46, 3 February 2010 (UTC)
More than 2 arguments in a function are not infrequent. A mathematical example is the hypergeometric function, which has 4 arguments, and which has a nice Wikipedia article. — Preceding unsigned comment added by 128.219.49.14 (talk) 23:03, 12 September 2012 (UTC)
Most stuff in math is not about finite sets, so there was a fair bit of stretch from that result to math in general. Also, can be expressed doesn't mean it's convenient to do it. The claim about computer science was even more silly. Just think of relational databases; most tables in practice have more than two or three columns. Tijfo098 (talk) 09:12, 27 November 2012 (UTC)

## Average Joe, and Math symbols

Would it be possible to edit this page with a few examples. I'm not against complex greek and roman math symbols, but most of the people I know glaze over when they see any complicated numbers.

Also, perhaps more context examples would be useful...

I agree. Let's have an example of some of these, at least one in arithmetic, and one for the bigger, um, things. Otherwise, this is not appropriate for a layman.

## Other Examples?

As an example of a ternary operator, perhaps modular exponentiation, dc has this built in. It's a bit more mathematical than the two current programming examples. mdclxvi 06:02, 8 July 2007 (UTC)

## Synonyms of arity

The synonyms of arity are given as adicity, type and rank. I would challenge the latter two. Types as used in programming include characteristics of components, not just their number. The type of a function is a different concept which includes the type of its return value. Rank conveys a sense of order of one thing bring of higher rank than another. Both of these words do not seem to really by synonyms of arity. (Adicity is fine as a synonym; a function that takes a variable number of arguments is variadic, for example.) Ablonus (talk) 13:23, 27 November 2008 (UTC)

I never heard of "variadic", and if I wanted to challenge anything it would be "adicity" - but Google Scholar has quite a few hits for that. Both "type" and "rank" are very plausible as synonyms for "arity" in some fields of mathematics, although it's hard to search for such uses. That "type" has another, unrelated, meaning in computer science is no more relevant than the fact that it also has another, unrelated, meaning in model theory (see type (model theory)). BTW, the most important synonym of "n-adic" seems to be missing because it doesn't have a version as a noun: "n-place". --Hans Adler (talk) 13:34, 27 November 2008 (UTC)
OK. I wasn't aware that they could be synonyms in some fields of mathematics so it's good you mentioned that. I can only comment on the computing side. The opening sentence which currently says, "In logic, mathematics, and computer science, the arity (synonyms include type, adicity, and rank) of a function..." makes it sound as though such synonyms apply to computer science (and, for that matter, to mathematics generally not just parts thereof). That does not seem to be a valid assertion. (By the way the most common example of a variadic function is C's printf. Being variadic it takes an indefinite number of arguments.) Ablonus (talk) 10:21, 28 November 2008 (UTC)
Ah, I must have heard this in the C context before. I don't agree with your reading of the parentheses. After all, we add synonyms for users who are more familiar with them than with the article title, not as a recommendation to actually use them. (Unless we do it in the article.) Therefore it doesn't seem really relevant in which fields the synonyms are used. --Hans Adler (talk) 13:46, 28 November 2008 (UTC)
That works well when dealing with one subject area or one discipline. In this case, however, three disciplines are mentioned specifically. In the very same sentence (the first) where the three areas of applicability are mentioned the article states that Type and Rank are synonyms. A person who did not know the topic would naturally, on reading this, understand that the synonyms are generally applicable. The first sentence does NOT make it clear that Type is a synonym of Arity only in the fields of mathematics and logic and not in computer science. (Presumably logic goes along with mathematics but maybe not.) Ablonus (talk) 15:08, 28 November 2008 (UTC)
Can this section of the discussion page be deleted now? The change being discussed was made more than a year ago. I'm not sure what the guidelines are for when to delete discussion sections. Ablonus (talk) 10:55, 20 March 2010 (UTC)
Is the term arity only colloquial use and adicity formal usage? Arity sounds a bit like this, but I am no native speaker. This might be indecated. --Munibert (talk) 21:05, 30 June 2010 (UTC)
No, they are both formal. Adicity is far less often encountered though, especially in math. Tijfo098 (talk) 08:47, 27 November 2012 (UTC)

The article says that the term "dyadic" less ambiguous than "binary",

... as illustrated by the term dyadic Boolean operator where boolean can be safely replaced by binary, but replacing dyadic by binary exposes the ambiguity.

I do not agree.

1. It is not safe (in the sense of "does not change the meaning") to replace "boolean" by "binary". A boolean operator is a function defined on B, the set of two truth values, or some (finite) power of B; a binary operator is an operator that takes two arguments (usually from the same set.
2. It is true that the term "binary" is used in other contexts, such as "binary arithmetic", where it does not refer to arity. But also "dyadic" is used in other contexts, such as dyadic rationals.

--Aleph4 (talk) 22:13, 18 May 2011 (UTC)

## ASM example wrong

The example under the ternary heading that uses assembly language is wrong: The notation employed implies AT&T syntax, so the source and destination operands are reversed; the instruction actually moves data from the AX register to memory. — Preceding unsigned comment added by 79.168.133.49 (talk) 03:09, 18 June 2014 (UTC)