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Math and science::Analysis::Tao::05. The real numbers

Nested intervals property for reals

Nested interval property

A sequence of nested closed intervals of reals has a [something something].

In other words, if one considers a sequence of nested closed intervals \( (I_n)_{n=0}^{\infty} \) such that for each \( n \in \mathbb{N} \), \( I_n = [a_n, b_n] \) for some \( a_n, b_n \in \mathbb{R} \) and \( I_{n+1} \subseteq I_n \), then It holds that [\( \cap_{n=1}^{\infty} I_n \;\; ? \quad  ? \;\;  \)].

Proof on the reverse.