Infinite Sets Definition
A set of elements A is said to be infinite if the elements of its proper subset A’ can be put into one-to-one correspondence with the elements of A.
If an infinite set can be put into one-to-one correspondence with the set of natural numbers, then the infinite set is called a countable infinite set otherwise it is called an uncountable infinite set.
Infinities can be of different sizes or levels, for example, a set of Real Numbers (R) is a larger infinity than a set of Natural or Rational Numbers, but both the set of natural numbers and rational numbers, are the same size sets, as both have the same cardinality.
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