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

Start with the Bolzano-Weiertrass theorem and use it to construct a proof of the Nested Interval Property.

2. Relevant equations

Bolzano-Weiertrass: Every bounded sequence contains a convergent sub-sequence

Nested Interval Property: Closed intervals nested inside of each other forever is non-empty.

3. The attempt at a solution

If we start with a bounded sequence on a closed interval and then we make it smaller we have a smaller portion of the sequence and so this smaller part must converge to something and we just keep making the interval smaller and we squeeze it down to a point, the sequence must converge to this point because it is the only point in the sequence.

Can I just start with some interval and slowly make it approach the middle by having it increase from the right and decrease to the left till I just have enclosed one point and make it converge to this point.

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# Homework Help: Nested Interval Proof:

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