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Consider the sequence $$\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},\ldots$$ For which numbers $b$ is there a subsequence converging to $b$?

  • 3
    Every number in $[0,1]$?2012-02-16
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    In fact that sequence are the rational numbers in $]0,1[$ ordered in a particular form. Do you know the accumulation points of the rational numbers?2012-02-16

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