Proving that m+n√2m+n\sqrt{2} is dense in R\mathbb R

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I am having trouble proving the statement:

Let S={m+n√2:m,n∈Z} Prove that for every ϵ>0, the intersection of S and (0,ϵ) is nonempty.

Answer

Hint: |√2−1|<1/2, so as n→∞ we have that (√2−1)n→? In addition to that use the fact that the set S is a ring, i.e. closed under multiplication and addition.

Attribution
Source : Link , Question Author : user11135 , Answer Author : Jyrki Lahtonen

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