Avoiding Rational Distances

Ashutosh Kumar

doi:rae/1403894908

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Home > Journals > Real Anal. Exchange > Volume 38 > Issue 2 > Article

2012/2013 Avoiding Rational Distances

Ashutosh Kumar

Real Anal. Exchange 38(2): 493-498 (2012/2013).

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Abstract

We show that for any set of reals $X$ there is a $Y \subseteq X$ such $X$ and $Y$ have same Lebesgue outer measure and the distance between any two distinct points in $Y$ is irrational.