Exponential of Zero/Proof 4

Theorem

$\exp 0 = 1$

Proof

This proof assumes the Definition of $\exp x$ as the unique continuous extension of $e^x$.

\(\ds \exp 0\)

\(=\)

\(\ds e^0\)

\(\ds \)

\(=\)

\(\ds 1\)

Definition of $x^0$, where $x \ne 0$

$\blacksquare$