4

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
  • 11,164
  • 4
  • 32
  • 36
user113562
  • 43
  • 3
  • 4
    Take a look [here](http://math.stackexchange.com/questions/1/different-kinds-of-infinities). – Arthur Dec 05 '13 at 05:09

1 Answers1

3

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
  • 47,594
  • 2
  • 81
  • 150
  • 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