Lebl-Basic-Analysis-I · Problem 1.4.7

Real Numbers

Mathematics · intervals-cardinality

Problem

Suppose SS is a set of disjoint open intervals in R\mathbb{R}. That is, if (a,b)∈S(a, b) \in S and (c,d)∈S(c, d) \in S, then either (a,b)=(c,d)(a, b) = (c, d) or (a,b)∩(c,d)=∅(a, b) \cap (c, d) = \emptyset. Prove SS is a countable set.

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