Thread: Ordered Integral domain...

Prove or disprove that if a,b E D and a>b, then a^2>b^2..
I know its a disprove because -2>-3 but (-2)^2<(-3)^2....but I just need to prove it in words...and I dont know if I could use the example to prove it! thanks...

Originally Posted by vedicmath

Prove or disprove that if a,b E D and a>b, then a^2>b^2..
I know its a disprove because -2>-3 but (-2)^2<(-3)^2....but I just need to prove it in words...and I dont know if I could use the example to prove it! thanks...

Of course you just disproved it--you gave a counterexample. (of course you'd want to preface it with with the usual operations is a field, thus an ID and ordered with the usual ordering yet.. etc.)