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January 17th, 2014, 02:22 PM   #1
Tau
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How does cardinality apply to real numbers?

Isn't cardinality a concept that concerns discrete quantities? How then can you talk about the cardinality of real numbers which are continuous?
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January 17th, 2014, 03:59 PM   #2
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Re: How does cardinality apply to real numbers?

Quote:
Originally Posted by Tau
Isn't cardinality a concept that concerns discrete quantities? How then can you talk about the cardinality of real numbers which are continuous?
The answer to your first question is no, so the second question is not a problem.

http://en.wikipedia.org/wiki/Cardinal_number
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January 18th, 2014, 02:19 AM   #3
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Re: How does cardinality apply to real numbers?

Quote:
Originally Posted by Tau
Isn't cardinality a concept that concerns discrete quantities?
No, in general. True if 'cardinality' is replaced by 'countable cardinality'.
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January 18th, 2014, 03:11 AM   #4
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Re: How does cardinality apply to real numbers?

Thanks for the replies. So, my problem is understanding the definition of cardinality of uncountable infinity/ continuum. So, my question is how does that follow from ZFC axioms? Or if it's a new definition what's the proof that it's consistent with ZFC.
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January 18th, 2014, 12:40 PM   #5
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Re: How does cardinality apply to real numbers?

http://en.wikipedia.org/wiki/Cardinal_number

Start here. Read the last section (continuum hypothesis) in particular.
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