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Math Help - prove or disprove

  1. #1
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    prove or disprove

    for all x,y in Real Number , that x > y , then there exists a number Z , such that x<z and z < y.


    I concluded this is a false statement because the inequality would be Z > x > y > Z which make no sense, but how to disprove this?.

    please help~
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: prove or disprove

    assume x > y, z > x and z < y,

    if x > y then x - y >0,

    since z < y then z - y < 0 < x - y so z - y < x - y and so z < x but we assumed z > x which is a contradiction
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