ADDENDUM--population data on unconfined cats is sorely lacking, particularly that of their rate of increase.  Having found additional estimates of this value, I'm adjusting my AVERAGE annual rate of population increase downwards from 43.2 million to 38 million.  This in no way invalidates the above argument that "adoption" is mathematically impossible.  It's just that I prefer to be honest and accurate, because the cat-nutters, outdoor cat-hoarders and TNR charlatans never are.