This is a continuation of the following questions:
http://answers.google.com/answers/threadview?id=743129
http://answers.google.com/answers/threadview?id=743424
I think I've figured out how to calculate g(a,x,y) where x and y are
of the form p/q and m/n where p,q,m,n are all integers greater than 0.
This doesn't solve the problem for irrational numbers like pi or e,
but I'm going one step at a time.
However, I've ended up at another dead end. I need to be able to calculate
g(a,n,-1) where a>0 and n is an integer greater than 0.
To calculate it, it must somehow be done such that no part of the
definition requires the calculation of g(a,x,y) where x or y are 0,
negative, or non-integers. The definition may use values of a larger
or smaller than the original a in g(a,n,-1) because I can calculate
that separately.
Examples using known lower operations:
g(0,x,-1) = x + -1 = x - 1
g(1,x,-1) = x * -1 = 0 - x
g(2,x,-1) = x ^ -1 = 1/x
If this isn't possible then I guess I need to give up on this line of
inquiry and try to define it in some other way. I've gotten lots of
reading material from the previous questions (I ordered one of the
books mentioned), so I'll have to dig further into that to see how to
address these issues. |