2+2=4

Yes, 2 + 2 = 4.

Quick justifications:

• Intuition: two objects plus two objects makes four objects.
• Formal (Peano) approach: use plus(0, n) = n and plus(n, S(m)) = S( plus(n, m) ).
  • 2 = S(S(0)) = 2, and 2 = S(1) with 1 = S(0).
  • plus(2, 2) = plus(2, S(1)) = S( plus(2, 1) )
  • plus(2, 1) = plus(2, S(0)) = S( plus(2, 0) ) = S(2) = 3
  • therefore plus(2, 2) = S(3) = 4

If you’d like, I can show similar steps for other operations or in different number systems (e.g., binary, modular arithmetic).