\begin{definition}[Definition:Set/Implicit Set Definition/Multipart Infinite Set]
Let $S$ be a set.
Suppose $S$ is to contain:
:$(1): \quad$ a never-ending list of elements
and
:$(2): \quad$ other elements which are unrelated to that list (perhaps another never-ending list).
Then a '''semicolon''' is used to separate the various conceptual parts:
:$S = \set {1, 3, 5, \ldots; 2, 4, 6, \ldots; \text{red}, \text{orange}, \text{green} }$
Note that ''without'' the semicolon it would appear as though the first list (of odd numbers) '''continued''' as the second list (of even numbers) which in turn '''continued''' as a list of colours, which is absurd.
Category:Definitions/Sets
\end{definition}