# Please look at this basic proof.

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• April 26th 2010, 05:21 PM
dag
Please look at this basic proof.
The question asks to prove, that if x,y $\in$R 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?
• April 26th 2010, 05:39 PM
Plato
Given that $x then $x<\frac{x+y}{2}