Editing Element (mathematics) (section)

==Sets==
Writing <math>A = \{1, 2, 3, 4\}</math> means that the elements of the set {{mvar|A}} are the numbers 1, 2, 3 and 4.  Sets of elements of {{mvar|A}}, for example <math>\{1, 2\}</math>, are [[subset]]s of {{mvar|A}}.

Sets can themselves be elements. For example, consider the set <math>B = \{1, 2, \{3, 4\}\}</math>. The elements of {{mvar|B}} are ''not'' 1, 2, 3, and&nbsp;4.  Rather, there are only three elements of {{mvar|B}}, namely the numbers 1 and 2, and the set <math>\{3, 4\}</math>.

The elements of a set can be anything. For example the elements of the set <math>C = \{\mathrm{\color{Red}red}, \mathrm{12}, B\}</math> are the color red, the number 12, and the set {{mvar|B}}.

In logical terms, <math>(x \in y) \leftrightarrow \forall x[P_x = y]: x \in \mathfrak D y</math>.{{clarify|date=December 2024}}