Hey all, need some help with the following proof:
Let A be a non-empty subset of Z and b ∈ Z, such that for each a ∈ A, b <= a. Then A has a smallest element.
All help appreciated!
Using what theorems? You can use either induction or the "well ordered" property of the positive integers to prove this. They are equivalent but I don't know which you have to use. In either case, I think I would start by looking at B= {a- b| a∈ A}, a set of positive integers.