This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: (upon expanding) ⇒ xxy =y ⇒ x (1y ) =y ⇒ x =y 1y = y y1 Now we return to the proof. ] Deﬁne x = y y1 . Then x ∈ R as y ∈ R { 1 } . Also, x 6 = 1. [ To check this: Assume for a contradiction that x = 1 . Then x = y y1 = 1 ⇒ y = y1 ⇒ 0 =1 , a contradiction. ] Thus x ∈ R { 1 } , the domain of f . We then have that f ( x ) = f ( y y1 ) = y y1 y y11 = y y( y1) = y 1 = y. Thus, for each y in the codomain, we can ﬁnd an x in the domain such that f ( x ) = y . Therefore, f is a surjection. 2...
View
Full Document
 Winter '10
 Spyros
 Domain of a function, X1, codomain

Click to edit the document details