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Unformatted text preview: tion and inverse relations oF Functions. The composition oF two Functions is always a Function. In contrast, we shall see that the inverse relation oF a Function need not necessarily be a Function. D EFINITION 4.14 (C OMPOSITION OF UNCTIONS ) Let A,B and C be arbitrary sets, and let f : A B and g : B C be arbitrary Functions oF these sets. The composition oF f with g , written g f : A C , is a Function defned by g f ( a ) def = g ( f ( a )) For every element a A . In Haskell notation, we would write (g.f) a = g (f a) It is easy to check that g f is indeed a Function. Notice that the co-domain oF f must be the same as the domain oF g For the composition to be well-defned. 36...
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- Spring '10