## Types of Numbers

Natural
Numbers

Natural numbers (often
denoted by

Integers**N**) consist of positive integers or counting numbers (1, 2, 3, ...) or, in some cases, non-negative numbers (0, 1, 2, 3, ...).Natural numbers have two main purposes: counting
("there are 2 dogs") and ordering ("that is the 4^{th}
largest planet").

Integers (often denoted
by

**Z**) consist of positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...), and the number zero. Integers are numbers that can be written without a fractional or decimal portion. The numbers 56, 112, -13 are integers while 33.43 and 3½ are not.Rational Numbers

A rational number
is a number which can be expressed as a ratio of two integers.
Non-integer rational numbers (commonly called fractions) are usually
written as

Irrational Numbers*a*/*b*, where*b*is not zero.An irrational number is any
real number that is not a rational number. Specifically, it
is a number which cannot be expressed as a fraction

*m*/*n*, where*m*and*n**n*non-zero. An example of an irrational number is π ≈ 3.141592653589793...