Definition:Set/Implicit Set Definition/Multipart Infinite Set

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Let $S$ be a set.

Suppose $S$ is to contain:

$(1): \quad$ a never-ending list of elements


$(2): \quad$ 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.