What are Finite Sets and Infinite Sets | Types of Sets | MathOGuide

What are Finite Sets and Infinite Sets | Types of Sets | MathOGuide

Finite sets and infinite sets are two fundamental concepts in set theory.

1. **Finite Sets**: A finite set is a set that contains a definite number of elements. In other words, you can count the elements in a finite set, and there are a finite number of them. For example, the set of integers from 1 to 5 {1, 2, 3, 4, 5} is a finite set.

2. **Infinite Sets**: An infinite set is a set that contains an unlimited or endless number of elements. These sets cannot be counted because they continue indefinitely. For example, the set of all natural numbers {1, 2, 3, 4, ...} is an infinite set because there is no largest natural number, and the set goes on forever.

Types of sets:
1. **Singleton Set**: A set that contains only one element.
2. **Empty Set (Null Set)**: A set with no elements.
3. **Subset**: A set that contains only elements that are also in another set.
4. **Universal Set**: A set that contains all the objects under consideration.
5. **Equal Sets**: Sets with the same elements.
6. **Equivalent Sets**: Sets with the same cardinality, meaning they have the same number of elements.
7. **Power Set**: The set of all subsets of a given set.
8. **Complement Set**: The set of all elements in the universal set that are not in a particular set.
9. **Intersection**: The set containing all elements that are common to two or more sets.
10. **Union**: The set containing all elements from all sets under consideration.