Alternating Sum and Difference of Binomial Coefficients for Given n/Lemma

Lemma for Alternating Sum and Difference of Binomial Coefficients for Given $n$

$\ds \sum_{i \mathop = 0}^0 \binom 0 0 = 1$

Proof

We have by definition of vacuous summation that:

$\ds \forall n \in \Z: n < 0: \sum_{i \mathop = 0}^n \binom n 1 = 0$

Then from Zero Choose Zero:

$\ds \sum_{i \mathop = 0}^0 \binom 0 0 = 1$

$\blacksquare$