Cardinality of The Continuum - Sets With Cardinality of The Continuum

Sets With Cardinality of The Continuum

A great many sets studied in mathematics have cardinality equal to . Some common examples are the following:

• the real numbers
• any (nondegenerate) closed or open interval in (such as the unit interval )
• the irrational numbers
• the transcendental numbers
• the Cantor set
• Euclidean space
• the complex numbers
• the power set of the natural numbers (the set of all subsets of the natural numbers)
• the set of sequences of integers (i.e. all functions, often denoted )
• the set of sequences of real numbers,
• the set of all continuous functions from to
• the Euclidean topology on (i.e. the set of all open sets in )
• the Borel σ-algebra on (i.e. the set of all Borel sets in ).