User:DPizzo/sandbox

= 1+1 (Elementary arithmetic) = 1+1 is an addition formula in which both addends are 1. It is often referred to as the simplest math problem, and used in a variety of metaphors. In elementary arithmetic, the answer is 2.

Proof
The proof starts with Peano's axioms, the definition of 1 as S(0) and 2 as S(1), and the definition of addition. Addition is defined such that: a+0=a and a+S(b)=S(a+b). From this we can prove that 1+1=2:

$$1+1=1+S(0)$$ (substituting definition of 1)

$$1+S(0)=S(1+0)$$ (application of addition)

$$S(1+0)=S(1)$$ (application of addition)

$$S(1)=2$$ (substituting defnition of 2)