Introduction to Sets

A set is a mathematical concept that represents a collection of well-defined objects. These objects are called the elements of the set.

In the example above, set A contains five elements: the numbers 1, 2, 3, 4, and 5.

Notation for Sets

• Sets are usually denoted by capital letters: A, B, C.
• Elements are listed in curly braces: A = {apple, pear, peach}.
• The ∈ symbol indicates that an element belongs to the set. For example: 3 ∈ A.
• The ∉ symbol indicates that an element is not part of the set. For example: 6 ∉ A.

Everyday Examples of Sets

• The fruits in your basket: {apple, pear, plum}.
• The days of the week: {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}.
• The students in the class: {Anna, Bence, Csilla, Dániel}.

Types of Sets

• Empty set (∅): contains no elements.
• Finite set: contains a finite number of elements, e.g., {1,2,3}.
• Infinite set: contains infinitely many elements, e.g., natural numbers: {1,2,3,...}.

Why Are Sets Useful?

Sets help organize and group things. Later in mathematics (for example, in probability and algebra), they play a fundamental role.

Practice Exercise