Subsection 2.3.8 (003V): Intersections of Families

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Table of Contents
Part 1: Sets
Chapter 2: Constructions With Sets
Section 2.3: Operations With Sets
Subsection 2.3.8: Intersections of Families (cite)

2.3.8 Intersections of Families

Let $\mathcal{F}$ be a family of sets.

Definition 2.3.8.1.1 ▶ Intersections of Families

The intersection of a family $\mathcal{F}$ of sets is the set $\bigcap _{X\in \mathcal{F}}X$ defined by

\[ \bigcap _{X\in \mathcal{F}}X\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft\{ z\in \bigcup _{X\in \mathcal{F}}X\ \middle |\ \text{for each $X\in \mathcal{F}$, we have $z\in X$}\webright\} . \]

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