Listed below are some of the most significant number sets.
- , also called counting numbers, are the numbers used for counting. The set of natural numbers is denoted by $\mathbb{N}.$
- are the natural numbers in addition to zero. The set of whole numbers is denoted by $\mathbb{W}.$
- are the whole numbers in addition to their opposite. The set of integer numbers is denoted by $\mathbb{Z}.$
- are the numbers that can be expressed as the ratio between two integers. The set of rational numbers is denoted by $\mathbb{Q}.$
- are the rational numbers, in addition to the numbers that cannot be expressed as the ratio between two integers. The set of real numbers is denoted by $\mathbb{R}.$
- are the numbers that can be written in the form $z=a+bi,$ where $a$ and $b$ are real numbers, and $i$ is the . The of a complex number is $a,$ and the is $b.$ The set of complex numbers is denoted by $\mathbb{C}.$
Note that there are other significant number sets not shown in the Venn Diagram above, including:
- are numbers that can be written in the form $a+bi,$ where $a$ is any real number, $b$ is a non-zero real number, and $i$ is the imaginary unit. This set is represented with the symbol $\mathbb{I}.$
- are the real numbers that cannot be expressed as the ratio between two integers. The set of irrational numbers can be written as $\mathbb{R}\setminus \mathbb{Q}.$
- are the that have exactly two : $1$ and themselves.