In mathematics, a set is a collection of distinct objects that is usually defined by a rule that determines whether an element is a member of a particular set. For example, a set could be defined to contain "all the odd numbers between 1 and 21" or the numbers "1, 3, 5 and 7".

The HashSet<(Of <(T>)>) class is based on the model of mathematical sets and provides high-performance set operations similar to accessing the keys of the Dictionary<(Of <(TKey, TValue>)>) or Hashtable collections. In simple terms, the HashSet<(Of <(T>)>) class can be thought of as a Dictionary<(Of <(TKey, TValue>)>) collection without values.

A HashSet<(Of <(T>)>) collection is not sorted and cannot contain duplicate elements. If order or element duplication is more important than performance for your application, consider using the List<(Of <(T>)>) class together with the Sort method.

HashSet<(Of <(T>)>) provides many mathematical set operations, such as set addition (unions) and set subtraction. The following table lists the provided HashSet<(Of <(T>)>) operations and their mathematical equivalents.

In addition to the listed set operations, the HashSet<(Of <(T>)>) class also provides methods for determining set equality, overlap of sets, and whether a set is a subset or superset of another set.

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