What Is Euler's Number e?

We are now going to look at the number $e$. $e$ is a very special number that shows up in many different applications in a variety of subjects, everything from nature to economics.

The number $e$ is an irrational number, which means that it can not be written as a fraction. The number is named after one of the most fascinating people in history, Leonhard Euler (1707–1783); it is called Euler’s number. Another name used for the number $e$ is the natural number.

In the box below you will see the definition of the number $e$. There are some new expressions as well, like $\underset{t\to 0}{\lim }$. You call this type of expression a limit, and it’s read as “the limit as $t$ approaches 0”.

You need limit values when you look at values that are infinitely small or large, because they are impossible to calculate with non-quantitative numbers. You can think of the expression in the box as “what happens to ${\left(1+t\right)}^{\frac{1}{t}}$ when $t$ becomes infinitely small?” The answer is that the expression becomes $e\approx 2.718281828\dots$.