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I learned from real analysis course that when we devide [0,1] into irrational part $I$ and rational part $R$, we have $m(R) = 0, m(I) = 1$.

So my question is, can I say we have zero probability that we pick rational number from $[0,1]$ segment?

My friend said no but I can't find why.

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    $\begingroup$ See this and this. $\endgroup$ – Thomas Shelby Mar 11 at 5:20
  • $\begingroup$ @ThomasShelby Thanks, So Can I say we cannot sample rational number at all in a real line In a uniform manner? is that the meaning of probability zero. $\endgroup$ – Peter Kim Mar 11 at 6:12

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