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January 17th, 2014, 02:22 PM  #1 
Member Joined: Jan 2014 Posts: 86 Thanks: 4  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?

January 17th, 2014, 03:59 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  Re: How does cardinality apply to real numbers? Quote:
http://en.wikipedia.org/wiki/Cardinal_number  
January 18th, 2014, 02:19 AM  #3  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: How does cardinality apply to real numbers? Quote:
 
January 18th, 2014, 03:11 AM  #4 
Member Joined: Jan 2014 Posts: 86 Thanks: 4  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.

January 18th, 2014, 12:40 PM  #5 
Global Moderator Joined: May 2007 Posts: 6,835 Thanks: 733  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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