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3.7 Set Types -- `set`, `frozenset`

A set object is an unordered collection of immutable values. Common uses include membership testing, removing duplicates from a sequence, and computing mathematical operations such as intersection, union, difference, and symmetric difference. New in version 2.4.

Like other collections, sets support `x in set`, `len(set)`, and `for x in set`. Being an unordered collection, sets do not record element position or order of insertion. Accordingly, sets do not support indexing, slicing, or other sequence-like behavior.

There are currently two builtin set types, `set` and `frozenset`. The `set` type is mutable -- the contents can be changed using methods like `add()` and `remove()`. Since it is mutable, it has no hash value and cannot be used as either a dictionary key or as an element of another set. The `frozenset` type is immutable and hashable -- its contents cannot be altered after is created; however, it can be used as a dictionary key or as an element of another set.

Instances of `set` and `frozenset` provide the following operations:

Operation | Equivalent | Result
--- | --- | ---
`len(s)` |  | cardinality of set s

`x in s` |  | test x for membership in s
`x not in s` |  | test x for non-membership in s
`s.issubset(t)` | `s <= t` | test whether every element in s is in t
`s.issuperset(t)` | `s >= t` | test whether every element in t is in s

`s.union(t)` | s | t | new set with elements from both s and t
`s.intersection(t)` | s & t | new set with elements common to s and t
`s.difference(t)` | s - t | new set with elements in s but not in t
`s.symmetric_difference(t)` | s ^ t | new set with elements in either s or t but not both
`s.copy()` |  | new set with a shallow copy of s

Note, the non-operator versions of `union()`, `intersection()`, `difference()`, and `symmetric_difference()`, `issubset()`, and `issuperset()` methods will accept any iterable as an argument. In contrast, their operator based counterparts require their arguments to be sets. This precludes error-prone constructions like `set('abc') & 'cbs'` in favor of the more readable `set('abc').intersection('cbs')`.

Both `set` and `frozenset` support set to set comparisons. Two sets are equal if and only if every element of each set is contained in the other (each is a subset of the other). A set is less than another set if and only if the first set is a proper subset of the second set (is a subset, but is not equal). A set is greater than another set if and only if the first set is a proper superset of the second set (is a superset, but is not equal).

Instances of `set` are compared to instances of `frozenset` based on their members. For example, "`set('abc') == frozenset('abc')`" returns `True`.

The subset and equality comparisons do not generalize to a complete ordering function. For example, any two disjoint sets are not equal and are not subsets of each other, so all of the following return `False`: `a<b`, `a==b`, or `a>b`. Accordingly, sets do not implement the `__cmp__` method.

Since sets only define partial ordering (subset relationships), the output of the `list.sort()` method is undefined for lists of sets.

Set elements are like dictionary keys; they need to define both `__hash__` and `__eq__` methods.

Binary operations that mix `set` instances with `frozenset` return the type of the first operand. For example: "`frozenset('ab') | set('bc')`" returns an instance of `frozenset`.

The following table lists operations available for `set` that do not apply to immutable instances of `frozenset`:

Operation | Equivalent | Result
--- | --- | ---
`s.update(t)` | s |= t | update set s, adding elements from t
`s.intersection_update(t)` | s &= t | update set s, keeping only elements found in both s and t
`s.difference_update(t)` | s -= t | update set s, removing elements found in t
`s.symmetric_difference_update(t)` | s ^= t | update set s, keeping only elements found in either s or t but not in both

`s.add(x)` |  | add element x to set s
`s.remove(x)` |  | remove x from set s; raises `KeyError` if not present
`s.discard(x)` |  | removes x from set s if present
`s.pop()` |  | remove and return an arbitrary element from s; raises `KeyError` if empty
`s.clear()` |  | remove all elements from set s

Note, the non-operator versions of the `update()`, `intersection_update()`, `difference_update()`, and `symmetric_difference_update()` methods will accept any iterable as an argument.

The design of the set types was based on lessons learned from the `sets` module.

See Also:

Comparison to the built-in set types
  Differences between the `sets` module and the built-in set types.