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"Suppose X, Y in R (Real Numbers), X < Y prove there exists Z in R such that X < Z < R."

I'm currently trying to prove that X + Y / 2 satisfies this but I'm getting stuck. I first show that X + Y / 2 cannot be = to either X or Y. I then try to show that X + Y / 2 is > X since X < Y but I cannot seem to tie this in. Any help would be appreciated.

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# Real Number Proof

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