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This is the question with the answer: enter image description here

I do not understand why always there exist a sequence of rationals and a sequence of irrationals that tends to $y$ as $n$ tends to $\infty$, on what mathematical fact the author depends in using this idea, could anyone explain this for me?

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This is true because the set of rational numbers is a dense subset of $\mathbb{R}$. Similarly for the set of irrational numbers.

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  • $\begingroup$ what about y is it rational or irrational or real? $\endgroup$
    – Emptymind
    Jun 15 '17 at 11:27
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    $\begingroup$ y is a real number. $\endgroup$
    – Hikaru
    Jun 15 '17 at 11:43

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