Continuum Hypothesis
The Continuum Hypothesis (CH) is a concept in set theory that addresses the size of infinite sets. Specifically, it posits that there is no set whose size is strictly between that of the integers (countably infinite) and the real numbers (uncountably infinite). In simpler terms, it suggests that there are two sizes of infinity: the size of all whole numbers and the larger size of all points on a line. The CH has been shown to be independent of the standard axioms of set theory, meaning it can neither be proven nor disproven within that framework.
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The Continuum Hypothesis is a mathematical proposition regarding sizes of infinite sets, specifically concerning the set of real numbers. It suggests there is no set whose size is strictly between that of the integers (countable infinity) and the real numbers (uncountable infinity). In simpler terms, it posits that you can only have two sizes of infinity: one that can be counted (like whole numbers) and a larger one that can't be fully listed (like all decimals), but nothing in between. This hypothesis has important implications in set theory and the foundations of mathematics.