theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers R {\displaystyle \mathbb {R} } , sometimes called the continuum...

(see picture). By a similar argument, N has cardinality strictly less than the cardinality of the set R of all real numbers. For proofs, see Cantor's diagonal...

the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states: "There is no set whose cardinality is...

, the cardinality of the power set of the natural numbers. The cardinality of the continuum is the size of the set of real numbers. The continuum hypothesis...

cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the infinite cardinal numbers have been introduced...

{\displaystyle \aleph _{0}} (the cardinality of the set of natural numbers), and the cardinality of the continuum, that is, the cardinality of the set R {\displaystyle...

that the second beth number ℶ 1 {\displaystyle \beth _{1}} is equal to c {\displaystyle {\mathfrak {c}}} , the cardinality of the continuum (the cardinality...

larger than the integers but smaller than the real numbers Cardinality of the continuum, a cardinal number that represents the size of the set of real numbers...

the cardinality of the continuum, whose value in ZFC may be any uncountable cardinal of uncountable cofinality (see Easton's theorem). The continuum hypothesis...

_{0}}>{\aleph _{0}}} . The continuum hypothesis states that there is no cardinal number between the cardinality of the reals and the cardinality of the natural numbers...