(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume the nested Interval property it true and use a technique similar to the one used to prove the Bolzano Weierstrass theorem, to give a proof of the axiom of completeness.

axiom of completeness: Every non-empty set of reals that is bounded above has a least upper bound.

3. The attempt at a solution

Suppose we knew of an upper bound for our set. and another point in our set. Now we bisect this interval. Now when we bisect this interval we could get an interval which only consisted of points in the set or get an interval that had some points in the set and some that aren't in the set. We will pick the interval that has some points in the set and some that are not. So we keep doing this forever and eventually we will chisel it down to a unique point and this will be the least upper bound. Is this the right approach?

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# Bounded sets

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