Numbers are used to classify, count and in the service of measurement. The most familiar are natural numbers: those that enable counting (cardinal numbers) and ordering (ordinal numbers). Examples of other types of numbers are the following:
* Complex numbers: in algebra, solutions to equations that cannot be resolved by real numbers
* Dimensionless numbers: those with no physical dimension or units (e.g., π is a dimensionless number as well as an irrational number also referred to as ‘pure numbers’). More precisely, they are numbers with the dimensions of 1. An important feature of such numbers is that they do not typically change if systems of measurements are altered (e.g., in changing from imperial to metric units). A specific example from fluid mechanics, but applicable to other dynamical systems, is a Rayleigh number
* Imaginary numbers: product of a real number and square root of -1. Zero is both an imaginary and real number
* Integer: whole number, not a fraction, that is both positive and negative
* Irrational numbers: those that cannot be written as fractions (e.g., π, √2). Attempting to write such numbers as decimals results in an endless number without recurring digits
* Prime numbers: a number only divisible by itself or 1 (e.g., 2, 3, 6, 7, 11 … Note that 2 is the only even prime number
* Rational numbers: those that can be written as a fraction in which the nominator and denominator are both integers (e.g., 1/3)
* Real numbers: those that can assume both positive and negative values with decimal places after the point (e.g., 2.55). Thus, they are the opposite of imaginary numbers