Infinite Set Examples
Some examples of infinite sets are:
- Natural Numbers: The set of natural numbers (N) represents the counting numbers, starting from 1 and going on infinitely (1, 2, 3, 4, …).
- Prime Numbers: The set of prime numbers is an infinite set that contains numbers greater than 1 that have no divisors other than 1 and themselves (e.g., 2, 3, 5, 7, 11, 13, …).
- Integers: The set of integers (Z) includes all positive and negative whole numbers and zero i.e., { . . . -3, -2, -1, 0, 1, 2, 3, . . .}.
- Rational Numbers: The set of rational numbers (Q) includes all numbers that can be expressed as a fraction of two integers, such as 1/2, -3/4, 5/7, etc.
- Irrational Numbers: The set of irrational numbers consists of numbers that cannot be expressed as a fraction of two integers, such as √2, π, and e.
- Real Numbers: The set of real numbers (R) contains all numbers, both rational and irrational, such as 3.14, √2, π, e, etc.
- Cantor Set: Cantor Set is a mathematical construct created by removing the middle third of a line segment repeatedly, forming an infinite set of points. It is self-replicating and has a surprising property of being uncountably infinite yet having zero length on the number line.
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