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:::::The term "co-range" is not used in recursion theory; it's a category-theory term. I think it was added here in an attempt to clarify for category theorists which meaning of "___domain" is intended. See [[___domain (mathematics)]] — Carl <small>([[User:CBM|CBM]] · [[User talk:CBM|talk]])</small> 19:46, 8 August 2008 (UTC)
(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)
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