[math-fun] Moore-Schulman base-3/2 conjecture

Hi Warren. Yes, we had noticed the "almost all x" argument. But we really need it to work for some explicit real, such as zero... Cris

--I'm suspecting hard. This is like the task of proving pi has all digit frequencies {0,1,2,3,4,5,6,7,8,9} equal -- a weaker statement than "normality" but still way way out of reach. --Perhaps it would be possible to go for a compromise result -- not as lame as "almost all x" but not as precise as "this specific x works: zero." See, "the almost all x" argument shows that the set of "red" x representable with (say) 5% or fewer nonzero digits, forms a Cantor-like measure-0 set. Unlike Moore I will not ask for the 5% to be true for every prefix, I'll merely ask it be true in the limit. This redefinition has some advantages I think for easier analysis. Namely: If some x and y are both red with threshold T (generalizing to arbitrary T not just 5%), then it follows that x+y also is red with threshold 2T. (I think. I have not fully checked, but I think with my redefinition you can prove various lemmas of that ilk.) OK, now the goal would be: can we find some finite set of numbers, related by some linear relations we design in, and argue that at least one of them must lie outside the red set defined by some threshold T>0? We won't say which one. That will be the compromise result. I'm proposing here a problem version which hopefully might be feasible to solve. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)