This preview shows pages 1–2. Sign up to view the full content.
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 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...
View Full Document
- Spring '10