Go backward to More Arithmetic
Go up to Top
Go forward to Difference
Same laws that also hold in N.
forall x in Z, y in Z: x+y = y+x.
Proof: Take arbitrary x in Z,y in Z. We have
x+y = (definition of +) I(x0 +N y0, x1 +N y1) = (commutativity of +N) I(y0 +N x0, y1 +N x1) = (definition of +) y+x.