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(unindent) The word "___domain" is ambiguous. According to [[Binary relation]], "''A binary relation R is usually defined as an ordered triple (X, Y, G) where X and Y are arbitrary sets (or classes), and G is a subset of the Cartesian product X × Y. The sets X and Y are called the ___domain and codomain, respectively, of the relation, and G is called its graph.''". Sometimes it is used to mean the set of things which might be considered as inputs to the function — in our case, the ___domain in that sense of a partial recursive function is always the natural numbers. Other times, ___domain (second sense) is used to mean the set of things within the ___domain (first sense) which when input to the function yields a value. This is what I was calling the "co-range" (for want of a better word) because the "range" of a function is the set of values which it outputs while the "co-___domain" is the set of things within which the co-range is located, that is, in our case, the natural numbers (again). [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 06:00, 9 August 2008 (UTC)
:Sure, ''___domain'' is ambiguous in general, but it's not ambiguous in recursion theory or descriptive set theory. In those fields it has a standard meaning. On the other hand ''co-range'' I have never heard of — Carl says it's a category-theory term, which is possible, but in my limited experience with category theory I've never come across it. We aren't supposed to make up language here. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 07:22, 9 August 2008 (UTC)
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