Show that the set of rational numbers is not order complete
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Let x be an irrational number , then take two rational sequences an and bn (rational sequences means that every term of that sequence is a rational number) such that both of them converge to x and an is less than or equal to bn for every natural n.
Then it's easy to show that sup(an)=inf(bn)=x but yet x is not a rational number therefore the set of rational numbers is not an order complete field
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