How can I prove |Q| = |N0| where Q is the set of positive rational numbers and N0 is the set of positive natural numbers with zero
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This statement is false. – Sean Nemetz May 10 '17 at 22:25
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Do you mean Q is positive rational numbers? – Laars Helenius May 10 '17 at 22:26
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can you briefly explain why? – Dhanush Rai May 10 '17 at 22:26
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$\mathbb Q$ typically represents the set of rational numbers, and in that case, indeed $|\mathbb Q| = |\mathbb N_0|$ – amWhy May 10 '17 at 22:26
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You can prove that $|\Bbb Q|=|\Bbb N|$ where $\Bbb Q$ is the set of rational numbers (or the positive rational numbers if you insist). The irrational numbers on the other hand are uncountable. – JMoravitz May 10 '17 at 22:27
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So if Q is a set of rational number then how can this statement be proved? – Dhanush Rai May 10 '17 at 22:30
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You can follow the link above, which will transport you to a the same question with seven anwsers, Dhanush. – amWhy May 10 '17 at 22:31
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Please google "proving the rationals are countable". This is a very very well known, much talked about and easy to research question. It's practically impossible for me to imagine you making any effort and not finding a solution somewhere. – fleablood May 11 '17 at 00:43