Exponential of One

Theorem

Let $\exp x$ be the exponential of $x$.

Then:

$\exp 1 = e$

where $e$ is Euler's number: $e = 2.718281828\ldots$

Proof

We have that the exponential function is the inverse of the natural logarithm function:

$\ln e = 1$

Hence the result.

$\blacksquare$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 14.4$