Iacchus said:
Well, I know that 1 + 1 = 2 because:
By definition natural numbers are the smallest set of numbers that fullfill the following axioms:
1. Zero is a number
2. If x is a number, then its successor f(x) is a number
3. Zero is not the successor of any number
4. If x and y are different numbers, then f(x) and f
are different numbers. So this is definition. Furthermore, by definition, the successor f(0) of zero is denoted by 1 and the successor f(1) is denoted by 2.
Next, the addition of two natural numbers is defined inductively using the following two rules:
(a) for all x, x + 0 = x; and
(b) for all x and y and z, if x + y = z, then x + f(x) = f(z).
Given the above three definitions we get:
(1) f(0) + 0 = f(0) (a)
(2) f(0) + f(0) = f(f(0)) (b)
Since the shorthand notation for f(0) is 1 and the shorthand for f(f(0)) = f(1) = 2, we can write (2) as 1 + 1 = 2.
But I still don't understand God.
