# Set

A set is an unordered array with no duplicates.

```erg
assert Set.from([1, 2, 3, 2, 1]) == {1, 2, 3}
assert {1, 2} == {1, 1, 2} # duplicates are automatically removed
assert {1, 2} == {2, 1}
```

Sets can perform mathematical set operations.

```erg
assert 1 in {1, 2, 3}
assert not 1 in {}
assert {1} or {2} == {1, 2}
assert {1, 2} and {2, 3} == {2}
assert {1, 2} not {2} == {1}
```

A set is a homogenous collection. Objects of different classes must be made equal in order to coexist.

```erg
s1 = {"a", 1, "b", -1} # TypeError
s2: {Int or Str} = {"a", 1, "b", -1}
```

## Set as Type

Sets can also be treated as types. Such a type is called an __Enum type_.

```erg
i: {1, 2, 3} = 1
assert i in {1, 2, 3}
```

The elements of the set are directly the elements of the type.
Note that the set itself is different.

```erg
mut_set = {1, 2, 3}.into {Int; !3}
mut_set.insert!(4)
```

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