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Unformatted text preview: R + Z + is defined as o ( x ) = ( x ) Note that order of composition matters: f o g g o f in general! Claim: If f : A B and g : B C are both onetoone, then g o f : A C is also onetoone Proof : Suppose x A , y A such that g o f ( x ) = g o f ( y ) By definition, g ( f ( x )) = g ( f ( y )) Since g is onetoone, this means that f ( x ) = f ( y ) Since f is onetoone, this means that x = y , which completes the proof...
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 Spring '10
 fleck

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