Naïve set theory MOC

Cardinality

The cardinality^[Mächtigkeit] of a set is a Cardinal uniquely corresponding to the set’s Isomorphism class within Category of sets. set

• iff there exists a bijection between sets and . and are thence said to be equinumerous.
• if and only if there exists an injection , or equivalently iff is equinumerous with some .

For finite sets, cardinality is given by the number of elements in the set. A set with is called countable. The naturals have the smallest transfinite cardinality.

Properties

• Upper bound on the cardinality of an arbitrary union

---

tidy | en | sembr