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Is it correct to say that

"A function or a map or a mapping is a binary relation such that ..."

Garrett
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    Depends on the author. –  Mar 26 '14 at 18:02
  • I'd think you'd write it as "function, map, or a mapping" – ruler501 Mar 26 '14 at 18:02
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    Yes. And also the phrases "taken as synonyms" and "taken to be synonymous" are synonymous. – rschwieb Mar 26 '14 at 18:02
  • Yes I wanted to make my question turn up more often in search results =D –  Mar 26 '14 at 18:10
  • Better to say: "A function is a binary relation such that ... . Functions may also be called maps or mappings. – GEdgar Mar 26 '14 at 18:14
  • I edited the title. Search engines are smart enough to realize that synonym and synonymous are synonymous, so you don't need to include keywords in a title. I couldn't find any Meta SE discussion on this topic although there is this one saying not to include tags in the title. – Garrett Mar 26 '14 at 20:21
  • @Mike: Could you give an example of an author who defines "function" and "map" differently? –  Mar 26 '14 at 22:57
  • @KennyLJ John Lee, "Smooth Manifolds", a function on a smooth manifold is (to him) a function $f: M \rightarrow \Bbb R^k$; a map is just in the set-theoretic sense (where it is, indeed, synonymous with function). –  Mar 26 '14 at 23:04
  • @Mike: Could you refer me to the book title and page number of this? It sounds like he is defining what a function on a smooth manifold is, which is a special type of function. So for example, you could likewise say that I define a real-valued function differently from a map, because a real-valued function is a map with the set of real numbers as the codomain. –  Mar 31 '14 at 12:55
  • @KennyLJ Yes, you're correct. I was only providing a context where the words weren't used for the same meaning. In a set-theoretic context I've never seen any author that uses these words differetly, in my meager experience. –  Mar 31 '14 at 15:54
  • Sometimes "map" or "mapping" specifically denotes a function that's continuous, smooth, etc. (depending on what category you're working in), while "function" means any function of sets. Then again, "function" also often gets employed in the former usage as well. – anomaly Jan 14 '15 at 04:22

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