In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis, advanced by Georg Cantor in 1877, about the possible sizes of infinite sets. It states: There is no set whose cardinality is strictly between that of the integers and that of the real numbers. Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's twenty-three problems presented in the year 1900. The contributions of Kurt Godel in 1940 and Paul Cohen in 1963 show that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo–Fraenkel set theory, the standard foundation of modern mathematics, provided set theory is consistent. The name of the hypothesis comes from the term the continuum for the real numbers.

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