Let {$\displaystyle x_n$}, $\displaystyle \ n \geq 1$, be a bounded sequence of real numbers and let x := sup{$\displaystyle x_n$ | $\displaystyle \ n \geq 1$}.

If for all n in N , $\displaystyle x_n$ < x, prove that x is an accumulation point of {$\displaystyle x_n$}

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