04/18/2008, 05:23 PM
bo198214 Wrote:I also didnt think about zeration in the context of the balanced mother law. We have (a+1)[0](a+1)=a+2 which changes to a[0]a=a+1 by substituting a+1=a. However this seems to contradict (a+2)[0](a+2)=a+4. So maybe there is no zeration here.
Yes, I completely agree with you. But I would prove it differently, as I did in an email to you awhile back.
\( x[n+1]2^t = f_n^t(x) \) as you mentioned, so
\( x[1]1 = f_0^0(x) = x \) because it is the identity function, but
\( x[1]1 = x + 1 \) by definition of addition!
therefore, \( f_0(x) = x[0]x \) cannot exist.
Andrew Robbins
