burak100 Posted September 21, 2011 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 ?????
DrRocket Posted September 21, 2011 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.
burak100 Posted September 21, 2011 Author 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
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