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Re: AN ERROR IN PEANO ARITHMETIC! x X [ s Y ] [ + X Z ] < x X Y Z
Posted:
Nov 5, 2013 10:38 PM


grahamcooper7@gmail.com writes: <snip> >> > But all of them require unlimited memory to perform unlimited size >> > number multiplication. >> >> It would be nice to see a proof. I don't have one. > > There is a proof but I don't recall it. > > The number of states of the machine is less than the > intermediate sums to perform multiplication. > > Starting with Least Significant Bit > > 010101010101 > X > 010101 > ____________ > > > Now you have X carry states, LEN(TERM2) > and only Y internal states.
That's an argument that one representation (I'm guessing  you don't actually give the input representation) and method fails. Whilst I am sure they all do, any argument for that must be more general.
To all intents a purposes, it probably suffices to say that neither
{ "x*y=z"  v(x) * v(y) = v(z) } { interleave(x, y, z)  v(x) * v(y) = v(z) }
is regular.
<snip>  Ben.



