One of the first important sets in mathematics comes from counting. When we count no objects, one object, two objects, three objects, and so on, we obtain the natural numbers, written $\mathbb N$:

$$\mathbb N=\lbrace 0,1,2,3,\ldots\rbrace.$$

Order and arithmetic

Each natural number represents a possible quantity. The natural numbers are ordered, so one quantity can be larger or smaller than another.

Adding or multiplying natural numbers always gives another natural number, which makes them a natural setting for basic counting and arithmetic.