Continuum

Mathematically, continuum can refer to the real line, its cardinality <math>\mathfrak{c}</math>, or any continuous connected dense linear order without endpoints. Generally, when mathematicians say "the continuum", they are referring to one of the first two possibilities (context clarifies which one). The Continuum Hypothesis conjectures that there is no set of cardinality bigger than that of the natural numbers <math>\aleph_0</math>, but smaller than the cardinality of the set of the real numbers <math>\mathfrak{c}</math>.