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Aug 8, 2015 at 20:23 comment added Anthony Quas OK - fair enough...
Aug 8, 2015 at 19:34 vote accept vizietto
Aug 8, 2015 at 19:02 comment added Adam P. Goucher @AnthonyQuas It certainly does -- that was the reason for including an empty interval between each pair of possibly-non-empty intervals in $K_1$. Note that we only consider the first 'digit' in which $x$ and $y$ differ, and treat the remaining 'digits' as an arbitrary real in $[0, 1]$.
Aug 8, 2015 at 18:20 comment added Anthony Quas Your answer doesn't seem to address the possibility that $x$ has some digits dominating those of $y$ and other digits with the reverse ordering.
Aug 8, 2015 at 17:49 history answered Adam P. Goucher CC BY-SA 3.0