Re: Complexity Theory for Simpletons (Collatz)

Craig Feinstein wrote:
Let me try to answer you without refering you to my papers. You can
just look at what I posted above. The place in my argument above where
it would break down for the n+1 modification is:

"Notice that you cannot algebraically reduce this formula to
anything simpler than itself, so in order to know this formula for a
specific n and m, it is necessary to know the values of a_1,...,a_k in
the formula."

This statement only is true with respect to the 3n+1 function, not the
n+1 function modification, since it can be further reduced when m is
large enough to 1 or 2.

I hope this helps.

Your argument is missing:

A theorem showing the non-existence of an algebra in which the
formula is reducible, and

A theorem that rules out proving general statements about things
unless we can algebraically reduce them.