Taking Rational Numbers at Random - Nicola Cufaro Petroni (AppliedMath, 2023)
In this article, some prescriptions to define a distribution on the set <semantics>Q0</semantics> of all rational numbers in <semantics>[0,1]</semantics> are outlined. We explored a few properties of these distributions and the possibility of making these rational numbers asymptotically equiprobable in a suitable sense. In particular, it will be shown that in the said limit—albeit no absolutely continuous uniform distribution can be properly defined in <semantics>Q0</semantics>—the probability allotted to every single <semantics>q∈Q0</semantics> asymptotically vanishes, while that of the subset of <semantics>Q0</semantics> falling in an interval <semantics>[a,b]⊆Q0</semantics> goes to <semantics>b−a</semantics>. We finally present some hints to complete sequencing without repeating the numbers in <semantics>Q0</semantics> as a prerequisite to laying down more distributions on it.