Definition:Indexed Iterated Binary Operation

Definition:Iterated Binary Operation Indexed

Definition
Let $\left({G, *}\right)$ be a magma.

Let $a, b \in \Z$ be integers.

Let $\left[{a \,.\,.\, b}\right]$ be the integer interval between $a$ and $b$.

Let $f : \left[{a \,.\,.\, b}\right] \to G$ be a mapping.

Degenerate case
Let $(G, *)$ be a unitary magma with identity $e$.

Let $a,b \in \Z$ be integers with $a<b$.

Then $\displaystyle\prod_{i=a}^b f(i) = e$.

Also known as
The indexed iterated binary operation of an ordered tuple is also known as their composite.

Also see

 * Definition:Indexed Summation