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Is there a name for functions like min, max, mean, sum which take $n$ numbers and maps them to one number? (In programming, they would probably be called variadic functions... I'm not too sure if this is the right term here)

Martin Thoma
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    I think that there is none; we use $\text{min}$ and $\text{max}$ ambiguously because we can easily recover from the context the number of arguments... (and in any case nothing change in their behaviour). – Mauro ALLEGRANZA Apr 25 '17 at 14:50
  • If we want to be formal, we have to use arity, as in computability theory where we have projection functions $U_i^n$ for every number $n$ of arguments. – Mauro ALLEGRANZA Apr 25 '17 at 14:52
  • I don't know such a word. But you can define all those you mention recursively as $f(head,tail)$ taking two arguments one element and the rest of the list. – mathreadler Apr 25 '17 at 14:54
  • In addition, we can always reduce them to the "basic" binary case $+(x,y,z)=+(+(x,y),z)$ and $\text {min}(x,y,z)= \text{min}(\text{min}(x,y), z)$ – Mauro ALLEGRANZA Apr 25 '17 at 15:05
  • @user275313 I think that term fits pretty well. Thank you :-) If you post it as an answer, I'll accept it. (And the question should then probably be moved to https://cs.stackexchange.com/ ) – Martin Thoma Apr 25 '17 at 15:40
  • Small note: the comments here about reducing to the binary case/implementing it recursively do not generally apply to these functions: in particular they do not apply to mean. – Mees de Vries Apr 26 '17 at 17:16
  • See @Avitus answer for more about "aggregation functions" https://math.stackexchange.com/a/923439/720890 – Clive Nov 01 '19 at 11:36

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There's no term I can think of used in mathematics, but in the context of SQL (the standard database query language) the term aggregating would be used to describe those functions, precisely for the property you mentioned, i.e. they take a value from multiple rows and return a single value.

By the way, if you check the Wikipedia article on Relational Algebra, (which is the mathematical formalism behind SQL), you can see that 'aggregation' is the term they use, and the functions you mention are four of the five standard functions they mention (you're missing count).

JonathanZ
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