# Exponential of Zero/Proof 5

## Theorem

$\exp 0 = 1$

## Proof

 $\ds \map \exp {z + \paren {-z} }$ $=$ $\ds \exp z \, \map \exp {-z}$ Exponential of Sum $\ds \leadsto \ \$ $\ds \map \exp {z - z}$ $=$ $\ds \dfrac {\exp z} {\exp z}$ $\ds \leadsto \ \$ $\ds \exp 0$ $=$ $\ds 1$

$\blacksquare$