# 5.15 `sets` -- Unordered collections of unique elements

New in version 2.3.

The `sets` module provides classes for constructing and manipulating unordered collections of unique elements. Common uses include membership testing, removing duplicates from a sequence, and computing standard math operations on sets such as intersection, union, difference, and symmetric difference.

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.

Most set applications use the `Set` class which provides every set method except for `__hash__()`. For advanced applications requiring a hash method, the `ImmutableSet` class adds a `__hash__()` method but omits methods which alter the contents of the set. Both `Set` and `ImmutableSet` derive from `BaseSet`, an abstract class useful for determining whether something is a set: `isinstance(obj, BaseSet)`.

The set classes are implemented using dictionaries. Accordingly, the requirements for set elements are the same as those for dictionary keys; namely, that the element defines both `__eq__` and `__hash__`. As a result, sets cannot contain mutable elements such as lists or dictionaries. However, they can contain immutable collections such as tuples or instances of `ImmutableSet`. For convenience in implementing sets of sets, inner sets are automatically converted to immutable form, for example, `Set([Set(['dog'])])` is transformed to `Set([ImmutableSet(['dog'])])`.

class `Set`( | [iterable])

  Constructs a new empty `Set` object. If the optional iterable parameter is supplied, updates the set with elements obtained from iteration. All of the elements in iterable should be immutable or be transformable to an immutable using the protocol described in section 5.15.3.

class `ImmutableSet`( | [iterable])

  Constructs a new empty `ImmutableSet` object. If the optional iterable parameter is supplied, updates the set with elements obtained from iteration. All of the elements in iterable should be immutable or be transformable to an immutable using the protocol described in section 5.15.3.

  Because `ImmutableSet` objects provide a `__hash__()` method, they can be used as set elements or as dictionary keys. `ImmutableSet` objects do not have methods for adding or removing elements, so all of the elements must be known when the constructor is called.