A set is a collection of distinct objects called elements. Order does not matter and repeated entries count only once. The universal set xi states which objects are under consideration. **Notation** | **Meaning** x in A, x A | An object belongs, or does not belong, to the set. n(A) | Number of distinct elements. | The empty set: no elements. A=B | The sets contain exactly the same elements. Example Let xi=1,2,3,4,5,6 and A=2,4,6. Then 4 in A, 3 A and n(A)=3. The set 6,2,4 equals A. A rule can describe a set: x in Z:1<x 4=2,3,4. Include the domain: integers and real numbers would give different sets. 0 has one element; has none. Braces describe a set, so 2 and 2 are different objects.

A set is a collection of distinct objects called elements. Order does not matter and repeated entries count only once. The universal set \(\xi\) states which objects are under consideration.

Let \(\xi=\{1,2,3,4,5,6\}\) and \(A=\{2,4,6\}\). Then \(4\in A\), \(3\notin A\) and \(n(A)=3\). The set \(\{6,2,4\}\) equals \(A\).

A rule can describe a set: \(\{x\in\mathbb Z:1<x\le4\}=\{2,3,4\}\). Include the domain: integers and real numbers would give different sets.

\(\{0\}\) has one element; \(\varnothing\) has none. Braces describe a set, so \(2\) and \(\{2\}\) are different objects.

Elements and set notation

Elements and set notation

Notation	Meaning
\(x\in A\), \(x\notin A\)	An object belongs, or does not belong, to the set.
\(n(A)\)	Number of distinct elements.
\(\varnothing\)	The empty set: no elements.
\(A=B\)	The sets contain exactly the same elements.