Part of the description of any real number is its sign; it can be positive, negative, or zero. When discussing a set of numbers, it can sometimes be helpful to know how to describe the sign of all numbers within the set.

Positive

A real number $n$ is said to be positive if it is greater than $0.$ $$\begin{array}{c}0<n<\infty \end{array}$$

Non-negative

Sets of numbers that are non-negative can include not only positive numbers but also $0.$ $$\begin{array}{c}0\le n<\infty \end{array}$$

Negative

Negative numbers are the opposite of positive numbers; a real number $n$ is said to be negative if it is less than $0.$ Adding a positive number and its corresponding negative will result in a sum of $0.$ $$\begin{array}{c}\text{-}\infty <n<0\end{array}$$

Non-positive

Similar to non-negative numbers, a set of numbers that are non-positive can include both negative numbers and $0.$ $$\begin{array}{c}\text{-}\infty <n\le 0\end{array}$$

Graphical Representation

Each of these sets of numbers can be represented with a number line inequality. Notice how the point at $0$ is closed when it is included in the set and open when it is not.