Prove 1 plus 1 equals 2?

Answer 1

# For every natural number x, x = x. That is, equality is reflexive. # For all natural numbers x and y, if x = y, then y = x. That is, equality is symmetric. # For all natural numbers x, y and z, if x = y and y = z, then x = z. That is, equality is transitive. # For all a and b, if a is a natural number and a = b, then b is also a natural number. That is, the natural numbers are closed under equality. # 0 is a natural number. # For every natural number n, S(n) is a natural number. # For every natural number n, S(n) ≠ 0. That is, there is no natural number whose successor is 0. # For all natural numbers m and n, if S(m) = S(n), then m = n. That is, S is an # If K is a set such that: #* 0 is in K, and #* for every natural number n, if n is in K, then S(n) is in K, then K contains every natural number. # If φ is a unary predicate such that: # #: #:* φ(0) is true, and #: #:* for every natural number n, if φ(n) is true, then φ(S(n)) is true, #: then φ(n) is true for every natural number n. Or. None of the above is relevant as... 1 + 1 = 3