Taking Rational Numbers at Random

In this article, some prescriptions to define a distribution on the set Q0 of all rational numbers in [0,1] 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 b...

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Bibliographic Details
Published in:AppliedMath 2023-09, Vol.3 (3), p.648-663
Main Author: Cufaro Petroni, Nicola
Format: Article
Language:English
Subjects:
discrete distributions
randomness
rational numbers
Online Access:Get full text
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Summary:In this article, some prescriptions to define a distribution on the set Q0 of all rational numbers in [0,1] 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 Q0—the probability allotted to every single q∈Q0 asymptotically vanishes, while that of the subset of Q0 falling in an interval [a,b]⊆Q0 goes to b−a. We finally present some hints to complete sequencing without repeating the numbers in Q0 as a prerequisite to laying down more distributions on it.
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath3030034