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​Here is a breakdown of the common categories of mathematical sets and an illustrative example.

​Types of Sets

​Sets in mathematics are typically categorized based on the number of elements they contain:

​1. Finite Set

​A Finite Set is a set whose elements can be counted, and the counting process comes to an end. In other words, it has a definite, limited number of elements.

​Examples: The set of days in a week, the set of students in a specific classroom.

​2. Infinite Set

​An Infinite Set is a set whose elements cannot be counted in a definite number. The counting process would never end. These sets have an unlimited number of elements.

​Examples: The set of all whole numbers (\{0, 1, 2, 3, \ldots\}), the set of all points on a line.

​3. Empty Set (or Null Set)

​The Empty Set is a unique set that contains no elements at all. It is denoted by the symbols \emptyset or \{\}.

​Example: The set of odd numbers divisible by 2.

​Other Important Types

​Singleton Set: A set that contains exactly one element. (e.g., \{5\})

​Equal Sets: Two sets are equal if and only if they contain exactly the same elements. (e.g., \{a, b, c\} and \{c, a, b\} are equal).

​Equivalent Sets: Two sets are equivalent if they have the same number of elements (same cardinality), even if the elements themselves are different. (e.g., \{1, 2, 3\} and \{a, b, c\} are equivalent).

​Example of a Set

​A common example to illustrate a set is the set of all vowels in the English alphabet. 
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