# Feinstein's Proof, Paraphrased and Inspected

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-Feinstein uses a string-based argument to show (by contradiction) that infinite
steps are required to prove Collatz's conjecture

-Use the (s,b,e) notation as the string to represent l.d.a.s growing in the abstract tree

-Now we have a nice string which never stops growing and models tree growth well

-The abstract tree contains an infinite set of infinite sets. AGREED!

-But we've analyzed the odd integer content of the abstract tree, finding that
it converges to complete coverage of the integers.

-Sometimes this looks paradoxical

-While the predecessor tree grows without limit in terms of its depth, the sum of
the densities of the integers it represents grows asymptotically to cover all the integers

-Feinstein is in league with those thinking the toad can't get out of his hole,
and that the overtaking runner can never pass.

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