Just a quick question:
If a = [A] and a belongs to N (set of all natural numbers) doesn't that mean that A is a subset of N?
The reason I'm asking this is because I'm trying to prove the theorem that the set of all natural numbers is closed under addition.
The definition of addition that I have is the following: Let a, b, c be natural numbers. We write a + b = c if and inly if there exists sets A and B such that a = [A], b = [B], A intersection B is nullset and c = [A union B]
I was thinking if a and b are natural numbers then A and B are subsets of N, and so is their union, which makes c also a natural number.
Thank you