Continuum (Set Theory)

In set theory, the continuum means the real numbers themselves, or the corresponding infinite cardinal number, often denoted by a script c. Georg Cantor proved that this cardinality is larger than aleph null, the smallest infinite cardinal, and further proved that it equals two raised to the power of aleph null, the cardinality of the power set of the natural numbers. The continuum hypothesis states that no cardinality lies strictly between that of the continuum and that of the natural numbers, equivalently that the cardinality of the continuum equals aleph one.