## 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 2^{i} multiples

-- 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(2^{i}/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

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