# Definition:Set/Implicit Set Definition/Multipart Infinite Set

## Definition

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:

- $S = \left\{{1, 3, 5, \ldots; 2, 4, 6, \ldots; \text{red}, \text{orange}, \text{green}}\right\}$

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.