Properties of Infinite Sets
Various properties of Infinite sets are discussed below,
- Any subset of a countable set is countable.
- A superset of an uncountable set is uncountable.
- If A is an infinite set (either countable infinite or uncountable infinite), then the set of A is uncountable infinite.
- The union of two or more countable sets is countable.
- The cartesian product of two countable sets is countable.
- If A is an uncountable infinite set and B is any set, then the cartesian product of A and B is also uncountable infinite.
- ℵ1 = 2ℵ0
Infinite Set
Infinte set is one of the types of Sets based upon the cardinality in Set Theory and sets are one of the important topics in mathematics. In simple words, an infinite set is a set with infinite elements i.e., the number of elements in an infinite set never depletes. This concept of infinite sets seems to be complicated at first sight but we’ll try our best to make it as comprehensive and understanding as possible.
This article deals with this concept and tries its best to explain the concept in detail. Other than that, this article covers definition, notation, types, cardinality, examples, and properties of Infinite Sets. So, let’s start learning about Infinite Sets.
Table of Content
- What are Infinite Sets?
- Infinite Sets Definition
- Infinite Set Notation
- Infinite Set Examples
- Types of Infinite Sets
- Properties of Infinite Sets
- Venn Diagram for Infinite Sets
- Difference Between Finite Sets and Infinite Sets