Definition:Universe (Set Theory)

Sets are considered to be subsets of some large universal set, also called the universe. Exactly what this universe is will vary depending on the subject and context.

When discussing particular sets, it should be made clear just what that universe is.

The usual symbol used to signify the universe is $$\mathfrak {A}$$. However, this is old-fashioned and inconvenient, so some newer texts have taken to using $$\mathbb{U}$$ instead.

With this notation, this definition can be put into symbols as: $$\forall S: S \subseteq \mathbb{U}$$