Exponential of Zero/Proof 2

Theorem

$\exp 0 = 1$

Proof

Using the definition of the exponential as a limit of a sequence:

\(\ds \exp 0\)

\(=\)

\(\ds \lim_{n \mathop \to \infty} \left({1 + \frac 0 n}\right)^n\)

\(\ds \)

\(=\)

\(\ds 1\)

$\blacksquare$