Question

State and prove Nested Interval theorem?​

Answer 1

Answer:

Hi itzmss

its your answer..

= The intervals are nested, i.e. I1 ⊇ I2 ⊇ I3 ⊇ ... ... So the theorem says that if the intervals are closed and satisfy (i) and (ii), then the intersection of all of the intervals cannot be empty, and in fact there is exactly one real number x which lies in all of them.

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