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Proposition: Limit of Nested Real Intervals

Let $(I_n)_{n\in\mathbb N}$ be nested real intervals. Then there is exactly one real number $x\in\mathbb R$ being their limit $$\lim_{n\to\infty}I_{n}=x.$$

Table of Contents

Proofs: 1

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016