Originally Posted by

**klmsurf** I'm reading through a book on Real Analysis (Intro.) and got a question on finite sets. The definition I'm using for a finite set is: a set A is finite iff there is a one-to-one function f on Nk onto A (Nk is read N sub k where k is a subscript and Nk is a subset of the natural numbers from 1 to k) for some k.

Question

Let A = {1, 2, 3, 2}, Nk = {1, 2, 3, 4}, and assume that f is bijective from Nk onto A. Observe that f(2) = f(4) implies 2 ≠ 4. It appears that f is not bijective. Is A finite or not? If A is finite, could you describe a bijective function f from Nk onto A.

Thanks