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Completeness axiom:
Every non-empty set of real numbers that is bounded above has a least upper bound.
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If the sequence ｢aₙ｣ is increasing, it has a least upper bound U.
For all ε>0 there exists a natural number N such that n>N ⇒ U−ε < aₙ.
U−ε < aₙ implies |aₙ−U| < ε.
So ｢aₙ Ƚn￫∞｣ = U.
The proof for a decreasing sequence is similar.
