Definition:Ordered Sum/General Definition

Definition
Let $S_1, S_2, \ldots, S_n$ be tosets.

Then we define $T_n$ as the ordered sum of $S_1, S_2, \ldots, S_n$ as:


 * $\forall n \in \N_{>0}: T_n = \begin {cases}

S_1 & : n = 1 \\ T_{n - 1} + S_n & : n > 1 \end {cases}$

Also see

 * Ordered Sum of Tosets is Totally Ordered Set: General Result