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Math Help - Order Among the Numbers

  1. #1
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    Order 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.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by noles2188 View Post
    1) Prove if x < y, then it is false that y < x;
    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)

    if x > y, then it is false that y > x.
    this is similar to the last one.

    2) Prove if x < y and z is a number, then x-z < y-z.
    Assume x < y. then that means x - y < 0. But x - y = x + 0 - y = x - z + z - y = x - z - (y - z) < 0

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