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.