Basic Analysis I — Real Analysis · Problem 1.4.3

Real Numbers — Jiri Lebl

Mathematics — Real Analysis · intervals

Problem

Prove Proposition 1.4.1. That is, suppose

I \subset \mathbb{R}

is a subset with at least 2 elements such that if

a < b < c

and

a, c \in I

, then

b \in I

. Prove that

I

is one of the nine types of intervals explicitly given in this section. Furthermore, prove that the intervals given in this section all satisfy this property.

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