Question

Claim: Prove that for every rational number z , there exists irrational numbers x and y such that x+y=z


Proof:

Suppose z=0 and for all irrational numbers x and y, x+y (not equal to) 0. Let x=-y, then by susbtitution x+y=-y+y=0. THis is a contradiction-x+y cannot equal 0. Thus for every rational number z, there exists irrational numbers x and y such that x+y=z