# Element (mathematics)

ru:Элемент множества
In mathematics, an **element** (also called a **member**) is an object contained in a set (or more generally a class).

Writing "*A* = {1, 2, 3, 4}", means that the elements of the set *A* are the numbers 1, 2, 3 and 4. Groups of elements of *A*, for example {1, 2}, are subsets of *A*.

Elements can themselves be sets. For example consider the set *B* = {1, 2, {3, 4} }. The elements of *B* are *not* 1, 2, 3, and 4. Rather, there are only three elements of *B*, namely the numbers 1 and 2, and the set {3, 4}.

The elements of a set can be anything. For example, *C* = {red, green, blue}, is the set whose elements are the colors red, green and blue.

The relation "is an element of", also called **set membership**, is denoted by "∈", and writing "*x* ∈ *A*", means that *x* is an element of *A*. Equivalently one can say or write "*x* is a member of *A*", "*x* **belongs** to *A*", "*x* is **in** *A*", or *A* **contains** *x*. The negation of set membership, is denoted by "∉".

Examples (using the sets defined above):

- 2 ∈
*A* - {3, 4} ∈
*B* - {3, 4} is a member of
*B* - 3 ∉
*B*

The number of elements in a particular set is a property known as cardinality, informally this is the size of a set. In the above examples the cardinality of the set *A* is 4, while the cardinality of the sets *B* and *C* is 3. An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements. The above examples are examples of finite sets. An example of an infinite set is the set of natural numbers.