Can one sample rational number from $[0, 1]$ in $\Bbb R$?

Asked Mar 11 '19 at 05:08

Active Mar 11 '19 at 05:14

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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.

edited Mar 11 '19 at 05:14

PrincessEev

asked Mar 11 '19 at 05:08

Peter Kim

1

See this and this. – cqfd Mar 11 '19 at 05:20
@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. – Peter Kim Mar 11 '19 at 06:12

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