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On the sums of elements of uncountable sets

  • Thread starter bbkrsen585
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  • #1
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I want to prove the following proposition:

Given any uncountable set of real numbers S, there exists a countable sub-collection of numbers in S, whose sum is infinite.

Please point me in the right direction.
 

Answers and Replies

  • #2
Office_Shredder
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As a small hint, consider for each n how many elements can have absolute value smaller than 1/n
 

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