Euler's Number

Euler’s number, denoted as , is a naturally occurring number related to exponential growth and exponential decay. The approximate value of Euler’s number is shown below.

However, when interpreting formulas and functions, this site considers Euler’s number as shorthand for the exponential function. This choice is intentional and hopefully leads to a deeper understanding of the math at play.

The numeric value is still very important and its connection to the exponential function is shown below.

This connection is discussed in-depth on the exponential function page.

Formal Definition

The value of is formally defined by the value of the exponential function at . Depending on which definition of the exponential function you are using, the value can either be calculated as a limit or a summation. This is shown below.