# Cantor–Bernstein theorem

(Redirected from Cantor-Bernstein theorem)
Because the second type class contains the countable ordinal numbers, which have cardinality ${\displaystyle \aleph _{1}}$, this result proves (by an inclusion of naturally defined sets) that ${\displaystyle \aleph _{1}\leq 2^{\aleph _{0}}}$, a relation between these two aleph numbers that (without assuming the axiom of choice) was not previously known.[1]