Density of a sequence in the unit interval

Asked Sep 05 '16 at 12:28

Active Sep 05 '16 at 12:28

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Let $\sqrt{a}$ be an irrational number for somepositive real number $a$. How can someone prove that the sequence $a_n$$=$$\{$$n$ $\sqrt{a}$$\}$ is dense in the interval $[0,1]$? Can someone help me out with a hint? Thank you in advance!

we denote by $\{a\}$$=a-[a]$

asked Sep 05 '16 at 12:28

Marios Gretsas

21,906

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I would guess the square-root was a distraction, and this is true for all irrationals – Henry Sep 05 '16 at 12:34
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For example http://math.stackexchange.com/questions/272545/multiples-of-an-irrational-number-forming-a-dense-subset – Henry Sep 05 '16 at 12:35
Yes indeed,you are right. thank you! – Marios Gretsas Sep 05 '16 at 12:36
A proof that I find simpler than the one in the duplicate can be found here. – Brian M. Scott Sep 05 '16 at 21:14

Density of a sequence in the unit interval

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