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Math Help - Real Numbers Inequality Proof

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    Real Numbers Inequality Proof

    Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

    Any thoughts on this proof?
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    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by jstarks44444 View Post
    Let x,y be elements of the Real Numbers such that x < y. There exists z in the Real Numbers such that x < z < y.

    Choose z=(1/2)(x+y) and use the standard arithmetic and ordering axioms of \mathbb{R} .
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