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Re: 0^0
Posted:
Oct 21, 2006 9:49 AM
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Akira Bergman wrote: Obviously the base can not be 1. The next logical
choice is 2. Boolean
is the minimum space.
Why not?
0 = .
1 = 1 = 1^1
2 = 11 = 1^2
3 = 111 = 1^3
In this notation, addition and subtraction is easy. Multiplication too,
as repeated addition.Division is then repeated subtraction.
Binomial coefficients were mentioned. Use vectors. Put a = 1, b = 1,
and you get the unit base. The products (a + b + ...+ n)^m generate
vector strings. Write the product, e. g. aaabc as the matrix A
(1,0,0)
(1,0,0)
(1,0,0)
(0,1,0)
(0,0,1).
Find the quadratic form with its transpose A' - A'A:
(3,0,0)
(0,1,0)
(0,0,1)
and/or the product with the unit vector row J'A
(3,1,1),
and you get the coordinate of the point, the string is going in.
Find the sums or differences of two strings, and you get incidence
matrices of unoriented or oriented graphs.
kunzmilan
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