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Unformatted text preview: a b c 1 2 3 A B E XAMPLE 4.9 The function f on natural numbers deFned by f ( x,y ) = x + y is onto but not one-to-one. To prove that f is onto, take an arbitrary n ∈ N . We must Fnd ( m 1 ,m 2 ) ∈ N × N such that f ( m 1 ,m 2 ) = n . This is easy since f ( n, 0) = n +0 = n . To show that f is not one-to-one, we need to produce a counter-example. In other words, we must Fnd ( m 1 ,m 2 ) , ( n 1 ,n 2 ) such that 34...
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- Spring '10