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| Math Central | Quandaries & Queries |
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Question from Justin, a student: Yes, I am reading the Paul Halmos book on Set theory, thanks for telling me how to get it! I was just wondering from your last answer though if the positive real infinity of calculus then corresponds to Aleph-null? I am sorry if this is a similar question to the one I asked before but I was just wondering about this! All the Best, Justin |
Justin:
The word "corresponds" does not have a well-defined meaning in this context. If you mean "are they the same thing," then no, they are not. If you mean "do they have something in common" then they do, in that each can be approached as a limit of finite numbers. But there are also many other ways in which they differ. For instance, aleph-null counts the elements of certain sets, and positive real infinity does not. Aleph-null is not a maximal element in the calss of cardinales (there is none), whereas positive real infinity is maximal in the closure of the reals.
Good Hunting
RD
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