Continuum (set theory)

Question

In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, c{\displaystyle {\mathfrak {c}}}. Georg Cantor proved that the cardinality c{\displaystyle {\mathfrak {c}}} is larger than the smallest infinity, namely, ℵ<!-- ℵ -->0{\displaystyle \aleph _{0}}. He also proved that c{\displaystyle {\mathfrak {c}}} equals 2ℵ<!-- ℵ -->0{\displaystyle 2^{\aleph _{0}}}, the cardinality of the power set of the natural numbers.