## Foundations of Mathematics## Set Theory |

## What is a set? |

Simply put, a set is a collection of objects or entities; these are called the *elements* of the set. The number of elements in a set can be large, small, finite, or infinite. The informal notation used for sets is sometimes seen as *x* = {*y*, *z*, …}, with brackets used to contain the elements within the set. It is stated as, “x is a set consisting of the elements y, z, and so on.” But more commonly, sets are seen as capital letters and elements as lowercase letters, such as *a* is an element of set *A*.