![]() ![]() The reals are uncountable that is: while both the set of all natural numbers and the set of all real numbers are infinite sets, there can be no one-to-one function from the real numbers to the natural numbers: the cardinality of the set of all real numbers (denoted \mathfrak c and called cardinality of the continuum) is strictly greater than the cardinality of the set of all natural numbers (denoted \aleph_0). The set of real numbers are uncountable (this is pretty complicated) These definitions are equivalent in the realm of classical mathematics.
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