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<x1. What is the limit of the ratio

limk|{xR|n<xn+1}{q1,q2,...,qk}||{xR|0<x1}{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 such n?

Answer

Attribution
Source : Link , Question Author : Hilbert7 , Answer Author : Community

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