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...
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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 $x < y$ add z to both sides $x + z < y+z$ Only If Assume $x+z<y+z$ then $x+z-z < y+z-z$ $x < y$ QED
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