The paradox of the continuum refers to a fundamental problem in set theory that highlights the relationship between different sizes of infinite sets, specifically questioning how there can be 'more' real numbers than natural numbers, despite both being infinite. This paradox arises from the comparison of countable and uncountable infinities, illustrating that while the set of natural numbers is infinite and countable, the set of real numbers is uncountably infinite, leading to contradictions in our understanding of infinity.
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