Just learned that 1 + 1 = 2 is unprovable under certain number frameworks

I find it interesting that a lot of basic mathematical facts like 1 + 1 = 2 are unprovable under certain number systems. To be more specific the framework I am referencing is Robinson Arithmetic. <br><br>Robinson Arithmetic is a simple axiomatic system that lacks the induction axiom, but is generally sufficient to prove basic facts like 1 + 1 = 2<br><br>Robinson Arithmetic has the following axioms: <br><br>1. 0 ≠ S(x)<br><br>2. S(x) = S(y) -> x = y<br><br>3. x + 0 = x<br><br>4. x + S(y) = S(x + y)<br><br>5. x * 0 = 0<br><br>6. x * S(y) = x + (x * y)