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.

Unitary Magma
If the tuple is empty, then the composite is assigned the value of the identity of the operation (if this is a structure with an identity, that is):


 * $\oplus_0 \left({\varnothing}\right) = e_S$

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

Also see

 * Definition:Indexed Summation