Show/Hide
Introduction

A set is a collection of elements, such as:
 A = {1, 2, 3, 4, 5}

A set does not have order:
 {1, 2, 3, 4, 5} is the same as {5, 4, 3, 2, 1}
 It is convenient to write the elements of a set in consecutive order, but this is only for convenience.

Every element in a set is unique, multiples of the same element are ignored:
 The set {1, 2, 2} has a size of 2, and is the same as {1, 2}
Notation

It is common for sets to be denoted by a uppercase letter, and for its elements to be wrapped in curly braces:k
LaTeX:\mathbf{A} = \{ 1, 2, 3, 4, 5 \}

Sets can also be defined using set builder notation:

A rule is used to show which elements are members of the set:
 The set A defined above would contain all even integers between 0 and 2000.
 The format of the rule is: (formula: conditions) or (formula conditions).
 If it is not specified as a condition, then it is assumed that a is a real number.

A rule is used to show which elements are members of the set:
Elements in a set
 Elements in a set are usually represented by a lowercase letter.

To demonstrate that an element is part of a set, we use the set membership symbol:
LaTeX:\mathbf{a} \in \mathbf{A}

This can also be done with proper elements:
LaTeX:\1 \in \{ 1, 2, 3, 4, 5 \}

To show that an element is not part of a set, we use the 'not member of' symbol:
LaTeX:6 \notin \{ 1, 2, 3, 4, 5 \}
The Empty Set
The Empty Set (or Null Set) is a set containing no items. It is represented by the empty set symbol:
LaTeX:
\varnothing = \{\}
Code
A = frozenset([1, 2, 3, 4, 5]) print(1 in A) # prints 'True' print(6 not in A) # prints 'True'