Zero Choose n

Theorem

 * $\dbinom 0 n = \delta_{0 n}$

where:
 * $\dbinom 0 n$ denotes a binomial coefficient
 * $\delta_{0 n}$ denotes the Kronecker delta.

Proof
By definition of binomial coefficient:


 * $\dbinom m n = \begin{cases}

\dfrac {m!} {n! \left({m - n}\right)!} & : 0 \le n \le m \\ & \\ 0 & : \text { otherwise } \end{cases}$

Thus when $n > 0$:
 * $\dbinom 0 n = 0$

and when $n = 0$:
 * $\dbinom 0 0 = \dfrac {0!} {0! \left({0 - 0}\right)!} = 1$

by definition of factorial.

Hence the result by definition of the Kronecker delta.