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 N.
- are the natural numbers in addition to zero. The set of whole numbers is denoted by W.
- are the whole numbers in addition to their opposite. The set of integer numbers is denoted by Z.
- are the numbers that can be expressed as the ratio between two integers. The set of rational numbers is denoted by 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 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 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 I.
- are the real numbers that cannot be expressed as the ratio between two integers. The set of irrational numbers can be written as R∖Q.
- are the that have exactly two : 1 and themselves.