That is, if a function's arity is the number of inputs it has, its __ is the number of outputs it has. (Fill in the blank.)
What's the term for the number of outputs a function has?
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$\begingroup$
functions
terminology
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0One. That is what you call the number of outputs a function has. It is sometimes written in symbols as 1. :) – 2012-08-02
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0In the usual definition, of course, functions have a single input and a single output, but if all elements of the domain are $k$-tuples for the same value of $k$, you might say you have a "function of $k$ variables" or a "$k$-ary operation" (though I don't think people usually use the words "arity" and "function" together, prefering to call functions "operations" when talking about arities), and you might want a term for the dual case, but I haven't heard any such name (if I had to make one up I'd say co-arity). It's not as popular an idea somehow, e.g., people prefer operads to PROPs. – 2012-08-02
3 Answers
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I am pretty sure, based on a Google search, that at least some people call this notion "coarity" (or "co-arity" if you want the pronunciation to be clearer).
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0Aha! That makes sense – 2011-07-28
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The question doesn’t arise: by definition a function has only one output.
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0Clearly you are not a FORTRAN programmer, where a function can return values in its argument list. Given F(A,B,C) it is possible for F to have a value and C to be returned as well. But I don't know if there is a term for it. – 2011-07-28
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0OK, understood. But if the output of the function is (always) an n-tuple, then n is the function's _____? – 2011-07-28
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2@ross: I don't believe there's a term for that. I'd just say function so-and-so returns an $n$-vector or an $n$-dimensional array or whatever... – 2011-07-28
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0@rossmeissl: Like J.M., I’m not aware of any such term and would simply name the type of output. – 2011-07-28
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0@Ross: 360 Assembler and PL/I, and that was over 40 years ago. But I don’t think that *returns* (for a programming language function) is really quite the same thing as *has as output* (for a mathematical function). – 2011-07-28
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0@Ross Millikan: Brian wanted to ping you but he notified rossmeisl... @Brian: The notification always goes to the last match (and the owner of the post) cases are ignored. So in such (rare) occasions as the present one you're best off typing the entire name to be sure.` – 2011-07-28
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0@Theo: Thanks for the help. I should have checked to see how it works, but I forgot to worry about it after my first comment. – 2011-07-28
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0An explanation of the basics can be found in [Hendrik's answer here](http://meta.math.stackexchange.com/questions/2063/ping-only-works-for-the-first). There you'll also find a link to the detailed specification which will certainly contain more than you ever wanted to know about that topic. – 2011-07-28
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A function is a mapping from elements in one set to another set. The "from" set is called the domain, and the "to" set is called the range.
f: Z -> Z (f maps integers to integers)
f: R -> C (f maps reals to complex numbers)
f: R -> {0,1} (f maps real numbers to either 0 or 1)
f: R -> {red, green, blue} (f maps real numbers to either red, green or blue)
We can also combine sets to create multi-dimensional sets
Z x Z := two tuple of integers (1,1) ; ( 2,2) , (1,3)
R x R x R := three tuple of real numbers (1.2, 1.5, 3.14159...) ; etc....
It also makes sense to talk about functions mapping from a set of tuples to a set of tuples.
f: Z x Z -> Z (mapping two tuples of integers to integer)
f: Z -> Z x Z ( mapping integers to two tuples)
tl;dr When you talk about functions which outputs mulitple arguments, you're really talking about functions which outputs a single element which is an n-tuple.