Sets

A mathematical set is a collection of, unordered, unique objects. For example,{ 🍋, 🍊, 🍈 } is a set, and { 🍋, 🍊, 🍊 } is also a set, but this is considered equal to the set { 🍋, 🍊} because repeated elements do not change the structure of the set.

Roster Notation

Sets are often notated with { } curly brackets. This is called roster notation or enumeration notation.

You can abbreviate sets that proceed is a predictable pattern by using an ... ellipse, for example {1, 2, 3, ..., 100} for a set of all integers up to 100.

Set Builder Notation

Sets can also be notated as a selection from a larger set according to a condition. In the example below the | pipe character is read as “such that” (a colon is also used here sometimes) and reads "F is a set of all numbers n, such that n is an integer in the range from 0 to 19 exclusive".

F = { n | n is an integer, and 0 < n < 19 }

Sets are usually named with capital letters, such as A and B.

Sets are equal if all their elements are the same. This called the extensionality of sets.

A set with only a single element is called a singleton set. { 🍊 } is an example of a singleton set.