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Today in class my professor mentioned that there are different types of infinity. This confused me at first because I always thought infinity is just infinity. What are the different types of infinity?

Matthew Conroy
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user113562
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1 Answers1

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Your professor was talking about the distinction between countable & uncountable sets, established by Cantor's diagonal argument. See also Aleph number, Beth number, equinumerosity, & Cantor's contributions to set theory.

Lucian
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  • There's not only different sizes of infinity, but indeed also different kinds of infinity. For example, the usage of the symbol $\infty$ in limits, series, one-point-compactifications, ... is not really about cardinalities of sets. – Hagen von Eitzen Dec 05 '13 at 06:54