Can the Universal Set be Defined as the Union of Two Sets?

[Kamataat]

Let's say I have to prove something about two sets and I want to make use of the notion of the universal set. Is it OK then to define the universal set as the union of these two sets?

- Kamataat

 

[EnumaElish]

Universal Set: A set fixed within the framework of a theory and consisting of all objects considered in this theory. Yes, you may define the universal set as the union of these two sets as long as your theory does not make use of the intersection of their complements (relative to some bigger set).

 

[phoenixthoth]

If you change your axioms and/or logic, you can have a genuine universal set.

http://math.boisestate.edu/~holmes/holmes/setbiblio.html

 

[philosophking]

Wouldn't you also have to union (in addition to the two sets) the intersection of the complements of the two sets?