 Continuum hypothesis

The continuum hypothesis asserts that every infinite subset of the real numbers is either countable or equinumerous with the real numbers, equivalently $2^{{\aleph }_0}={\aleph }_1$.

The Continuum Hypothesis (CH) is a statement in set theory that deals with the size of infinite sets, particularly the sizes of the set of natural numbers and the set of real numbers. Formulated by Georg Cantor in the late 19th century, it posits that there is no set whose cardinality (size) is strictly between that of the integers and the real numbers.