Infinity invites resistance. Aristotle rejected the existence of the infinite entirely; to him, infinity was simply a limit that could never be reached, not a true mathematical entity. In the early 17th century, Galileo wrote that typical ways of thinking about sets and numbers held no meaning in the realm of the infinite, and that mathematicians would only find paradoxes if they tried to apply their usual tool kit to it. And when, 200 years later, Georg Cantor formalized the idea that infinity
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