Sets¶

A set is an unordered collection of unique elements.

Sets are useful when the main concern is not order, but membership and uniqueness.

flowchart TD
    A[set]
    A --> B[unordered]
    A --> C[unique elements]
    A --> D[fast membership testing]

1. Creating Sets¶

Sets can be written with braces.

colors = {"red", "green", "blue"}

An empty set must be created with set().

empty = set()

Using {} creates an empty dictionary, not a set.

print(type({}))
print(type(set()))

Output:

<class 'dict'>
<class 'set'>

2. Uniqueness¶

Sets automatically remove duplicates.

data = {1, 2, 2, 3, 3, 3}
print(data)

Output:

{1, 2, 3}

This makes sets very useful for eliminating repeated values.

3. Membership Testing¶

Sets are especially good for membership checks.

vowels = {"a", "e", "i", "o", "u"}

print("a" in vowels)
print("z" in vowels)

Output:

True
False

4. Set Operations¶

Sets support important mathematical operations.

Example:

a = {1, 2, 3}
b = {3, 4, 5}

print(a | b)
print(a & b)
print(a - b)
print(a ^ b)

Output:

{1, 2, 3, 4, 5}
{3}
{1, 2}
{1, 2, 4, 5}

Each operator also has a method form: union(), intersection(), difference(), symmetric_difference().

In-place variants update the set directly instead of creating a new one. The pattern extends to all operators.

a = {1, 2, 3}
a |= {4, 5}
print(a)

Output:

{1, 2, 3, 4, 5}

5. Common Set Methods¶

remove(x) raises KeyError if x is not in the set. discard(x) does nothing if x is absent. pop() raises KeyError on an empty set.

Example:

s = {1, 2, 3}

s.remove(2)
print(s)

s.discard(99)
print(s)

s.discard(3)
print(s)

Output:

{1, 3}
{1, 3}
{1}

6. Worked Examples¶

Example 1: remove duplicates¶

nums = [1, 2, 2, 3, 3]
unique = set(nums)
print(unique)

Output:

{1, 2, 3}

Example 2: membership test¶

allowed = {"admin", "editor"}

if "admin" in allowed:
    print("granted")

Output:

granted

Example 3: intersection¶

a = {"red", "green"}
b = {"green", "blue"}

print(a & b)

Output:

{'green'}

7. Common Pitfalls¶

Expecting order¶

Sets are unordered collections. Do not rely on iteration order.

s = {3, 1, 2}
print(s)

On CPython, small integer sets may appear sorted due to hash values, but this is an implementation detail and must not be relied upon.

Using {} for an empty set¶

{} creates a dictionary, not a set. Always use set() for an empty set, as shown in Section 1.

Assuming all objects can be stored in a set¶

Set elements must be hashable. Mutable types like lists and dictionaries cannot be added to a set.

s = set()
s.add([1, 2])

Output:

TypeError: unhashable type: 'list'

Python also provides frozenset, an immutable variant that is itself hashable and can be stored inside another set. See Hashing and Hash Tables for a full explanation.

8. Summary¶

Key ideas:

• sets store unique elements
• sets are unordered
• membership testing is a major strength of sets
• set operations reflect mathematical set ideas
• frozenset provides an immutable, hashable alternative

Sets are especially useful for uniqueness, filtering, and fast membership logic.