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February 16th, 2013, 04:07 AM  #1 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Discrete Mathematics  Set Theory
Hi all f is a function from R to N (from the real numbers, to the natural numbers) we are asked to prove there is a value k in N so that anyone has an idea? 
February 16th, 2013, 05:58 AM  #2 
Member Joined: Jan 2013 Posts: 93 Thanks: 0  Re: Discrete mathematics – set theory
We have . Since is uncountable, at least one of the must be uncountable (otherwise we would have a countable union of sets that are at most countable, which would be at most countable).

February 16th, 2013, 06:19 AM  #3 
Senior Member Joined: Jul 2012 Posts: 225 Thanks: 0  Re: Discrete Mathematics  Set Theory
I thought so to, but when I asked my professor, he told me that if i add aleph0+ aleph0 an infinite amount of times, it's not sure at all that i will get aleph0. he said there is another solution that bypasses this problem but i cant find it.


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