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 ).
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