This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full Document
 Spring '10
 fleck
 Logic, Philosophy of language, Inverse function, R+

Click to edit the document details