Cardinality

Upper bound on the cardinality of an arbitrary union

Let {𝐴𝑘}𝑘∈𝐾 be a collection of sets such that |𝐴𝑘| ≤𝜆 for all 𝑘 ∈𝐾 and |𝐾| =𝜅. Then¹ set

∣⋃𝑘∈𝐾𝐴𝑘∣≤𝜆𝜅

Proof

proof

---

develop | en | SemBr

Footnotes

1. 2008. Advanced Linear Algebra, p. 16 ↩