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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 one-to-one, then g o f : A → C is also one-to-one 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 one-to-one, this means that f ( x ) = f ( y ) Since f is one-to-one, this means that x = y , which completes the proof...
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- Spring '10
- Logic, Philosophy of language, Inverse function, R+