My math book has a definition and I'm a little confused. It says a set A is finite if and only if there is a one-to-one function f on A into N_k (a subset of the naturals read as N sub k). If I have a set A = {1, 2, 3, 3, 3, 4}, it's clearly finite with 6 elements, but it has the number 3 repeated three times. A 1-1 function f is a function such that f(i) = f(j) only when i=j. I guess I'm missing something incredibly simple, my questions are
1. Does there exist a 1-1 function of A, if so, can you give an example of this function?
2. Is A finite?
1. Does there exist a 1-1 function of A, if so, can you give an example of this function?
2. Is A finite?