The set of rational numbers in [0,1]

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SUMMARY

The set of rational numbers in the interval [0,1] is neither closed nor open. The boundary of this set is defined as the closed interval [0,1], as every open ball centered at any point t within this range contains both rational and irrational numbers. This confirms the density of rational numbers within the real numbers in this interval.

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yifli
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this set is neither closed nor open, correct? the boundary of this set is the closed interval [0,1] because every ball centered at 0<=t<=1 contains both rational numbers and irrational numbers, am I right?
 
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Hi yifli! :smile:

What you said is entirely correct!
 

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