> ## Documentation Index > Fetch the complete documentation index at: https://docs.syntblaze.com/llms.txt > Use this file to discover all available pages before exploring further. # Python frozenset A `frozenset` is a built-in Python data type representing an immutable, unordered collection of unique, hashable elements. It serves as the immutable counterpart to Python's standard `set` type, meaning its internal state and element composition cannot be modified after instantiation. Because a `frozenset` is immutable and Python strictly requires all of its elements to be hashable, the `frozenset` itself is hashable. This characteristic allows a `frozenset` to be used as a dictionary key or as an element within another `set`—operations that are impossible with a standard mutable `set`. ## Instantiation Because it is immutable, a `frozenset` must be populated at the time of creation using the `frozenset()` constructor. The constructor accepts a single optional iterable argument. Attempting to instantiate a `frozenset` with unhashable elements (such as lists or dictionaries) immediately raises a `TypeError`. ```python theme={"dark"} # Empty frozenset empty_fs = frozenset() # Instantiation from an iterable (list) # Duplicates are automatically discarded fs_from_list = frozenset([1, 2, 3, 2, 1]) # Result: frozenset({1, 2, 3}) # Instantiation from a string fs_from_string = frozenset("hello") # Result: frozenset({'h', 'e', 'l', 'o'}) # Utilizing hashability: frozenset as a dict key and set element fs_key = frozenset(['a', 'b']) my_dict = {fs_key: "value"} my_set = {fs_key, frozenset([1, 2])} ``` ## Technical Characteristics * **Immutability:** Once created, elements cannot be added, removed, or altered. * **Hashability:** Unlike a standard `set`, a `frozenset` implements a `__hash__()` method. Because Python enforces that all elements within any set type must be hashable, a `frozenset` is guaranteed to evaluate to a constant hash value. * **Unordered:** Elements do not maintain insertion order. Consequently, a `frozenset` does not support indexing, slicing, or other sequence-like behaviors. * **Uniqueness:** It strictly enforces element uniqueness. Duplicate values passed during instantiation are ignored. ## Supported Operations A `frozenset` supports all non-mutating mathematical set operations. These operations evaluate the elements and return a new `frozenset` or a boolean value, leaving the original objects unchanged. ```python theme={"dark"} fs_a = frozenset([1, 2, 3]) fs_b = frozenset([3, 4, 5]) # Union (Returns elements in either set) fs_a | fs_b # frozenset({1, 2, 3, 4, 5}) fs_a.union(fs_b) # Intersection (Returns elements common to both sets) fs_a & fs_b # frozenset({3}) fs_a.intersection(fs_b) # Difference (Returns elements in fs_a not in fs_b) fs_a - fs_b # frozenset({1, 2}) fs_a.difference(fs_b) # Symmetric Difference (Returns elements in either set, but not both) fs_a ^ fs_b # frozenset({1, 2, 4, 5}) fs_a.symmetric_difference(fs_b) # Relational Checks (Returns boolean) fs_a <= fs_b # False (issubset) fs_a >= frozenset([1, 2]) # True (issuperset) fs_a.isdisjoint(fs_b) # False (True if no common elements) ``` ## Unsupported Operations Because a `frozenset` is immutable, it lacks the in-place mutating methods found on a standard `set`. Attempting to invoke any of the following methods will raise an `AttributeError`: ```python theme={"dark"} fs = frozenset([1, 2, 3]) # The following methods are undefined for frozenset: fs.add(4) fs.remove(2) fs.discard(1) fs.pop() fs.clear() fs.update([4, 5]) ```

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