Alternating Sum and Difference of Binomial Coefficients for Given n/Proof 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:
 * $\ds \sum_{i \mathop = 0}^0 \binom 0 0 = 1$

For $n > 0$:

Hence the result.