Concrete generator style

A style of formal definition that defines a set as a union of a sequence $\begin{array}{l}{S}_0\\ subseteq{S}_1\\ subseteq\\ dots\end{array}$ where each $S_{i+1}$ is built from $S_i$ using rules - e.g., for naturals: $\begin{array}{l}{S}_0=\\ emptyset\end{array}$

A style of formal definition that defines a set as a union of a sequence $S_0\subseteq S_1\subseteq \dots$ where each $S_{i+1}$ is built from $S_i$ using rules - e.g., for naturals: $S_0=\varnothing$, $S_{i+1}=S_i\cup 0\cup succ(n)|n\in S_i,\mathbb{N}=\bigcup S_i$.