在数学中，连续统假设（德语：Kontinuumshypothese；英语：Continuum hypothesis，简称CH）是一个猜想，也是希尔伯特的23个问题的第一题，由康托尔提出，关于无穷集的可能大小。其为：

康托尔引入了基数的概念以比较无穷集间的大小，也证明了整数集的基数绝对小于实集的基数。康托尔也就给出了连续统假设，就是说，在无限集中，比自然数集{0，1，2，3，4......}基数大的集合中，基数最小的集合是实数集。而连续统就是实数集的一个旧称。

更加形式地说，自然数集的基数为（读作「阿列夫零」）。而连续统假设的观点认为实数集的基数为（读作「阿列夫壹」）。于是，康托尔定义了绝对无限。

In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states:

The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. Τhe answer to this problem is independent of ZFC set theory (that is, Zermelo–Fraenkel set theory with the axiom of choice included), so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940.