The cardinality of the continuum, often denoted by \(c\), is the cardinality of the set R of real numbers. [1]A set of cardinality \(c\) is said to have continuum many elements
Cantor’s diagonal argument shows that \(c\) is uncountable. Furthermore, it can be shown that R is equinumerous with the power set of N, so \(c=2^{\aleph_0}\). It can also be shown that \(c\) has uncountable cofinality
It can also be shown that \(c = c^{\aleph_0} = \aleph_0 c = cc = c + \kappa = c^n\)
for all finite cardinals \(n \ge 1\) and all cardinals \(\kappa < c\)