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 $b$?
Consider the sequence $\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{1}{4},\frac{2}{4},\frac{3}{4},\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},\ldots$
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sequences-and-series
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3Every number in $[0,1]$? – 2012-02-16
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2In 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