## What fraction of fractions does Cantor’s famous sequence enumerate?

Cantor’s famous sequence 11,12,21,13,31,14,23,32,41,15,51,16,… provides a bijection between natural numbers and positive rational numbers or cancelled fractions. About half of the fractions qi lie within 0<x≤1. What is the limit of the ratio limk→∞|{x∈R|n<x≤n+1}∩{q1,q2,…,qk}||{x∈R|0<x≤1}∩{q1,q2,…,qk}| for n \in \mathbb{N}? Is there an n for which the limit is 0? And if so, what is the first … Read more