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Math Help - Please look at this basic proof.

  1. #1
    dag
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    Please look at this basic proof.

    The question asks to prove, that if x,y  \inR and x<y then there must exist at least one z such that x<z<y.

    My question is can I do the following:
    suppose x,y are a subset of the real numbers with the set ranging from x<y. Then there must exist a z, an element of the above subset such that z=x+h. Then, x<z<y because if this was not the case then the set would not be bounded by x and y.

    While I know the proof is informal does it work?
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    Given that x<y then x<\frac{x+y}{2}<y
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