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Is there a nonempty perfect set in $R$ which contains no rational number? Its the excercise of Principles of Mathematical Analysis by Walter Rudin. I can't find the answer.I try to construct a set as cantor set but I can't prove it has no rational number or maybe it doesn't exist .Can anyone give me a hint ?I thought abt it for a whole day.


marked as duplicate by B. Mehta, Henno Brandsma, Namaste, Xander Henderson, cansomeonehelpmeout May 11 '18 at 18:35

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  • $\begingroup$ @B.Mehta Its in$R^2$.I just want to know that in$R^1$.I just began to study mathematical analysis of 1 dimension. $\endgroup$ – CJWHQ May 11 '18 at 13:27
  • $\begingroup$ I don't copy others.feel so bad to post a question in Stack.never on line again!wuwuwu $\endgroup$ – CJWHQ May 11 '18 at 13:47
  • $\begingroup$ @CJWHQ Don't worry, no-one's suggesting you copied! The duplicate vote means that the question's already been asked, so you can get a quicker answer by reading that instead of waiting for new replies here. Have a look at Henno's link - I'm pretty sure it answers your question :) $\endgroup$ – B. Mehta May 11 '18 at 14:26

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