2alephnull
2^{aleph_0}, commonly denoted c and referred to as the continuum, is a central cardinal in set theory. It is the cardinality of the set of real numbers, and is also the cardinality of the power set of the natural numbers, P(N), as well as the set of all infinite binary sequences {0,1}^N. In all these senses, 2^{aleph_0} measures the size of continuous mathematical objects.
Cantor’s diagonal argument shows that 2^{aleph_0} is strictly larger than aleph_0, meaning the real numbers are
The continuum hypothesis (CH) is the assertion that 2^{aleph_0} = aleph_1, i.e., that the continuum is the
In practice, 2^{aleph_0} is often treated as the cardinality of the real line, the continuum, and serves