Informally a restriction, of a function f is the result of trimming its domain. More precisely if S, is any subset, of X. The restriction of F to S is the function f | S from S to Y such that f | S (s) = f (s) for all s in S. If G is a restriction. Of F then it, is said that f is an extension of G.The overriding of F: X - > Y by G: W - > Y (also called overriding Union) is an extension of G denoted as (f ⊕ g): (X ∪ W). - > Y. Its graph is the set-theoretical union of the graphs of G and f | X W. Thus it relates, any element of the domain of. G to its image under g and any, other element of the domain of F to its image under f. Overriding is an associative operation;? It has the empty function as an identity element. If f | X ∩ W and G | X ∩ W are pointwise equal (e.g, the domains of F and. G are disjoint), then the union of F and G is defined and is equal to their overriding Union. This definition agrees with. The definition of Union for binary relations.
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