Continuum Hypothesis
The Continuum Hypothesis states that there is no set whose cardinality is strictly between that of the set of natural numbers (denoted by ℵ₀) and the set of real numbers (denoted by C i.e., Continuum). This is proposed by the great mathematician Georg Cantor in 1878 as part of his groundbreaking work on the theory of infinite sets.
The Continuum Hypothesis can be stated as follows:
- ℵ₀ = |N| (cardinality of the natural numbers)
- C = |R| (cardinality of the real numbers)
The Continuum Hypothesis claims that there is no set A such that ℵ₀ < |A| < C.
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