Unformatted text preview: → X be an injective function. Deﬁne a sequence of functions, called g n : X → X , for all n ∈ N , by the following rule: • When n = 0, and x ∈ X , then we deﬁne g ( x ) = x . • If n ≥ 1, and x ∈ X , then we deﬁne g n ( x ) = f ( g n1 ( x )). In other words, g n is the function obtained by repeating the function f , n times. Prove that, for every n ∈ N , the function g n is injective....
View
Full Document
 Fall '08
 Weissman
 Math, Remainder, Ring, Natural number, Even and odd functions, Injective function

Click to edit the document details