is xVx always true? that is, is it true that |x^{2}- x^{2}| < 2?

what does it mean for xVy to imply yVx? (hint: note that |x^{2}- y^{2}| = |-(x^{2}- y^{2})| = |y^{2}- x^{2}|).

transitivity will be the hardest thing to prove. think about the smallest possible difference of the squares of two (unequal) integers. which unequal integers can possibly be related by V?

(for example, do we have 2V3? 1V2? -3V4?)