burak100 Posted September 21, 2011 Share Posted September 21, 2011 f:R-->Q show that there is a q \in Q such that f^-1(q) is infinite set in R ????? Link to comment Share on other sites More sharing options...
DrRocket Posted September 21, 2011 Share Posted September 21, 2011 f:R-->Q show that there is a q \in Q such that f^-1(q) is infinite set in R ????? This appears to be homework. What do you know about cardinality ? This is a relatively simple exercise in the theory of cardinal numbers. Link to comment Share on other sites More sharing options...
burak100 Posted September 21, 2011 Author Share Posted September 21, 2011 Ok. I think; we have \mathbb{R}= \bigcup\limits_{q \in \mathbb{Q}} f^{-1}(q) , and we suppose that for all q in Q , f^{-1}(q) finite, then union would be countable but R is uncountable so contradiction... right?ITEX Link to comment Share on other sites More sharing options...
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