Symbols:Set Theory/Set Intersection/Family of Sets

Intersection of Family

$\ds \bigcap_{i \mathop \in I} S_i$

Let $I$ be an indexing set.

Let $\family {S_i}_{i \mathop \in I}$ be a family of sets indexed by $I$.

Then the intersection of $\family {S_i}$ is defined as:

$\ds \bigcap_{i \mathop \in I} S_i := \set {x: \forall i \in I: x \in S_i}$

The $\LaTeX$ code for \(\ds \bigcap_{i \mathop \in I} S_i\) is \ds \bigcap_{i \mathop \in I} S_i .

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Appendix $14$: Symbols