a tad more on OR-numbrals

Jens Voss jens.voss at poet.de
Fri Dec 21 10:03:39 CET 2001

Marc LeBrun wrote:
> [...lots of interesting thoughts on different numbral systems]

What strikes me most about the different numbral arithmetics is
that on one hand they are all nice since they are associative,
commutative and distributive, so the "divides" relation is
compatible with addition and multiplication. On the other hand,
the OR-numbral system appears to be the only one in which there
is no unique factorization, so as one consequence of that we have
to have to distinguish between "irreducible" and "prime" elements:

[5] for example is irreducible (since it is not a product of two
factors different from [1]), but not prime since it neither divides
[3] nor [11] but their product [3] * [11] = [31] = [5] * [7].


Jens Voss, POET Software, Kattjahren 4 - 8, 22359 Hamburg
The opinions expressed above are mine, not my employer's.
"Tee-dah, tah-dee, tee-dah, tah-dee..."
                    J. Brahms, 4th symphony, 1st movement

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