frozenset

class frozenset([iterable])

Return a new set or frozenset object whose elements are taken from iterable. The elements of a set must be hashable. To represent sets of sets, the inner sets must be frozenset objects. If iterable is not specified, a new empty set is returned.

Instances of set and frozenset provide the following operations:

len(s)

Return the number of elements in set s (cardinality of s).

x in s

Test x for membership in s.

x not in s

Test x for non-membership in s.

isdisjoint(other)

Return True if the set has no elements in common with other. Sets are disjoint if and only if their intersection is the empty set.

issubset(other)

set <= other

Test whether every element in the set is in other.

set < other

Test whether the set is a proper subset of other, that is, set <= other and set != other.

issuperset(other)

set >= other

Test whether every element in other is in the set.

set > other

Test whether the set is a proper superset of other, that is, set >= other and set != other.

union(other, ...)

set | other | ...

Return a new set with elements from the set and all others.

intersection(other, ...)

set & other & ...

Return a new set with elements common to the set and all others.

difference(other, ...)

set - other - ...

Return a new set with elements in the set that are not in the others.

symmetric_difference(other)

set ^ other

Return a new set with elements in either the set or other but not both.

copy()

Return a 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 and so does set('abc') in set([frozenset('abc')]).

The subset and equality comparisons do not generalize to a total ordering function. For example, any two nonempty 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.

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

Set elements, like dictionary keys, must be hashable.

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:

update(other, ...)

set |= other | ...

Update the set, adding elements from all others.

intersection_update(other, ...)

set &= other & ...

Update the set, keeping only elements found in it and all others.

difference_update(other, ...)

set -= other | ...

Update the set, removing elements found in others.

symmetric_difference_update(other)

set ^= other

Update the set, keeping only elements found in either set, but not in both.

add(elem)

Add element elem to the set.

remove(elem)

Remove element elem from the set. Raises KeyError if elem is not contained in the set.

discard(elem)

Remove element elem from the set if it is present.

pop()

Remove and return an arbitrary element from the set. Raises KeyError if the set is empty.

clear()

Remove all elements from the set.

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

Note, the elem argument to the __contains__(), remove(), and discard() methods may be a set. To support searching for an equivalent frozenset, the elem set is temporarily mutated during the search and then restored. During the search, the elem set should not be read or mutated since it does not have a meaningful value.