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Math Help - Real Analysis Proof

  1. #1
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    Real Analysis Proof

    Prove that if x is in set Q (all rational numbers), y is in set Q and x < y, then there is some z in set Q such that x < z < y.


    It is certain that if x<y then x cannot be greater than or equal to y.. also z can between x and y because there can be repeating decimals, and say x is 4 and y is 4.1, then there must always be a z that is in between these numbers... even if its 4.09999999999999 (repeating). I don't know how to write this in the form of a proof. Can anyone help?

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  2. #2
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    OH! Come on will you.
    a < b\, \Rightarrow \,a < \frac{{a + b}}{2} < b
    That is true for all real numbers a\;\&\;b.
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