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February 16th, 2013, 05:07 AM   #1
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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?
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February 16th, 2013, 06:58 AM   #2
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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).
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February 16th, 2013, 07:19 AM   #3
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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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