1) Prove if x < y, then it is false that y < x; if x > y, then it is false that y > x.

2) Prove if x < y and z is a number, then x-z < y-z.

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- April 26th 2009, 09:09 PMnoles2188Order Among the Numbers
1) Prove if x < y, then it is false that y < x; if x > y, then it is false that y > x.

2) Prove if x < y and z is a number, then x-z < y-z. - April 26th 2009, 09:53 PMJhevon
Assume x < y, and assume to the contrary that y < x. since x < y, we have x - y < 0. But also, since y < x, we have x - y > 0. this is a contradiction. (it violates the law of tricotomy)

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if x > y, then it is false that y > x.

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2) Prove if x < y and z is a number, then x-z < y-z.

adding y - z to both sides, we obtain the desired result.