Finite set

Definition

A set $A$ is finite when there is a natural number $n$ such that $A$ is equinumerous with $\{1, 2, \dots, n\}$. For $n = 0$, this set is the empty set. The number $n$ is unique, and it is the number of elements of $A$.

Remarks

Subsets, finite unions, finite products and the power set of finite sets are finite. A finite set is not equinumerous with any proper subset of itself. This is the pigeonhole principle. A set that is not finite is infinite.

Explanations

L1 human

A set is finite when you can count its elements and stop. The set of planets of the Solar System is finite, and so is the set of primes less than $100$.