I know that the definition of completeness is that a set contains the limits of rational numbers.(adsbygoogle = window.adsbygoogle || []).push({});

and I know the definition of convergence is that for all e>0 there exists N such that for n>=N |xn - x| < e where x is the limit of the sequence.

how to combine the two?

thanks in advance

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# How to write a mathematically rigorous definition of completeness

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