iff the sequence $(S_i)_{i \in \mathbb{N}, i < n}$ for some $n \in \mathbb{N}$ with $S_i = S_0 \otimes S_{i-1}$ for $0 < i < n$ and some combination operator $\otimes$ is an adaptation sequence.

Note that we could define the property of self-adaptation more generally by again constructing an index set on the sequence $(S_i)$ instead of using $\mathbb{N}$, but chose not to do so to not further clutter the notation. For most practical purposes, the adaptation is going to happen in discrete time steps anyway. It is also important to be reminded that despite its notation, the combination operator $\otimes$ does not need to be symmetric and likely will not be in this case, because when constructing $S_0 \otimes S_{i-1}$ we usually want to pass the previous instance $S_{i-1}$ to the general optimization algorithm encoded in $S_0$.[^3] Furthermore, it is important to note that the constant sequence $(S)_{i \in \mathbb{N}}$ is an adaptation sequence according to our previous definition and thus every system is self-adaptive with respect to a combination operator $X \otimes Y =_\text{def} X$. However, we can construct non-trivial adaptation sequence using partial orders $\sqsubset$ and $\prec$ instead of $\sqsubseteq$ and $\preceq$. As these can easily 