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Dec 11, 2015 at 4:44 comment added bof Your first question is answered by some of the answers to this old question of yours, for instance, this answer of mine.
Dec 10, 2015 at 23:09 history edited Stefan Kohl CC BY-SA 3.0
Improved the formatting of the question.
Jun 4, 2015 at 11:42 vote accept Dominic van der Zypen
Jun 4, 2015 at 10:42 answer added Stefan Kohl timeline score: 4
Jun 4, 2015 at 7:48 comment added Dominic van der Zypen Many thanks, Anthony - do you want to post your construction as a (partial) answer?
Jun 4, 2015 at 7:28 comment added Anthony Quas The first one is certainly 1. For a trivial construction, let $n_1\ll n_2\ll n_3\ll\ldots$. Then if $A=[n_1,n_2]\cup [n_3,n_4]\cup [n_5,n_6]$ while $B=\{0\}\cup [n_2,n_3]\cup [n_4,n_5]\cup\ldots$, their union is everything, but both have lower density 0.
Jun 4, 2015 at 6:35 history asked Dominic van der Zypen CC BY-SA 3.0