Indexed Summation over Interval of Length One

Theorem
Let $\mathbb A$ be one of the standard number systems $\N,\Z,\Q,\R,\C$.

Let $a\in\Z$ be an integer.

Let $f : \{a\} \to \mathbb A$ be a mapping on the singleton $\{a \}$.

Then the indexed summation:


 * $\displaystyle \sum_{i \mathop = a}^{a} f(i) = f(a)$

Proof
We have:

Also see

 * Indexed Summation over Interval of Length Two
 * Summation over Singleton Set