Calculus: Understanding Infinity in Context

Basically, infinity, written as $\infty$, represents a quantity larger than all numbers, yet, paradoxically, it is not a number itself. It is the approached value of the input of a function as it gets larger and larger. This is denoted by

$\lim_{x \rightarrow \infty}f(x)$

In a similar vein, $-\infty$ is smaller than all numbers, but is not a number itself. As the input of a function gets continually smaller, said input approaches $-\infty$, denoted as

$\lim_{x \rightarrow -\infty}f(x)$

Infinity is an extremely powerful concept in more advanced mathematics courses and should not be treated as a number by any means.