burak100
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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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f:R-->Q show that there is a q \in Q such that f^-1(q) is infinite set in R ?????