Add Up Those (a,b) Pair Contributions to the Total Integer Density
-- the cardinalities in the rows of sets (varying a but sharing b) of
the 2^a*3^b*n+c formulas exhibit the Fibonacci series or its 2i multiples
return to slide index
-- this provides a way to determine that all integers are present in the predecessor tree
-- the known sum(F(i)/2(i+1),i=1..infinity)=1 where F(i) are the Fibonacci numbers
-- make proper allowance
for offsets and multiples among the F(i) in the cardinality table
-- whence the total density will be the
sum(2i/3(i+2),i=0..infinity) or 1/2
-- 1/2 of all the integers is exactly the density required to cover
all odd integers.
-- if one considers the powers-of-2 multiples of every odd number
on the binary predecessor tree, and sums their densities, they total 1/2 also.
-- thus every positive integer, half even and half odd, is accounted for in a fine-grained analysis