Assume x is greater than y by z and y is greater than x by z (seems impossible, and it might very well be, but read on)

x> or equal to y

y> or equal to x

x=y+z

y=x+z

y=y+z+z

0=2z

0=z

x=y+z

x=y+0

x=y

I think what I just said is that if x is greater than y and y is greater than x, they must be greater than eachother by zero, thus proving they are equal. It also works if x is greater than y by z and y is greater than x by say q (though in the end both q and z are zero).

Does this make any sense?