Number Set

A number set is a collection of numbers that allows different types of numbers to be placed in various categories. Listed are some of the most common number sets.

• Natural Numbers, also called counting numbers, are the numbers used for counting. The set of natural numbers is denoted by N.
• Whole Numbers are the natural numbers in addition to zero. The set of whole numbers is denoted by W.
• Integer Numbers are the whole numbers in addition to their opposites. The set of integer numbers is denoted by Z.
• Rational Numbers are the numbers that can be expressed as a ratio between two integers. The set of rational numbers is denoted by Q.
• Irrational Numbers are the numbers that cannot be expressed as the ratio between two integers. The set of irrational numbers can be written as R\ Q.
• Real Numbers include rational numbers in addition to irrational numbers. The set of real numbers is denoted by R.
• Imaginary Numbers 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.
• Complex Numbers are the numbers that can be written in the form z=a+bi, where a and b are real numbers, and i is the imaginary unit. The real part of a complex number is a, and the imaginary part is b. The set of complex numbers is denoted by C.

Note that complex numbers include both the real numbers and the imaginary numbers. In the following table, each set will be shown by using the roster notation.