In the context of a theory or a problem, the set of all elements considered.

If a mathematical statement contains one or more variables, the universal set of these variables is the set of values that we can substitute for them.

The universal set is often simply called the **universal**.

### Notation

The symbol generally used to represent the universal set of a situation is \(\textrm{U}\).

### Examples

- If we are interested in the addition of odd whole numbers, the universal set is the set of whole numbers \(\mathbb{N}\).
- If we are interested in the whole solutions to the equation
*x*+ 4*y*= 144, then the universal set is \(\mathbb{Z}\). - Consider set E = {5, 6, 7} dans un ensemble \(\textrm{U}\) = {0, 1, 2, 3, 4, 5, 6, 7}.
- The set \(\textrm{U}\) is the universal set of set E.