1. ## Proof

Prove that x < y, if and only if x + z < y + z

My work so far:

Suppose x < y and z >0.
By definition, y-x and z are an element of the positive numbers (P).

Then I get lost on how to do the rest of the proof...

2. ## Re: Proof

Originally Posted by AwesomeHedgehog
Prove that x < y, if and only if x + z < y + z

My work so far:

Suppose x < y and z >0.
By definition, y-x and z are an element of the positive numbers (P).
If

Assume $x < y$

$x + z < y+z$

Only If

Assume $x+z<y+z$ then

$x+z-z < y+z-z$

$x < y$

QED