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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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This note was uploaded on 01/23/2010 for the course MATH Math2009 taught by Professor Koskesh during the Spring '10 term at École Normale Supérieure.
- Spring '10