Sets

Definition

A set is a collection of objects. This collection can be ifinte or inifinte. Mathematical objects are abstract, have properties, and can be acted upon by operations.

Set-builder notation

Other set notation

An important symbol in set notation is $\in$, which denotes membership. And $\notin$ means the object is not a member of the set.

The next symbol to consider is used to denote subsets. If $X$ and $Y$ are sets, and every element of $X$ is also an element of $Y$, then:

• $X$ is a subset of $Y$, denoted by $X \subseteq Y$
• $Y$ is a superset of $X$, denoted by $Y \supseteq X$

Important sets of numbers

• $\mathbb{N}$, which is the set of natural numbers defined as {0, 1, 2, 3, …}. This is the first set of numbers you learn as a child, and they are used for counting.
• $\mathbb{Z}$,
• $\mathbb{Q}$,
• $\mathbb{R}$,
• $\mathbb{C}$,