Re: Proposal: 6NF

Cimode wrote:
> Aloha Kakuikanu wrote:
> > Translating it into programming his simplest case, natural numbers and
> > integers, there are at least 5(!) classes involved:
> Yep. But the question is why 5 and not N? It's a problem I have been
> chewing on the last few years...No satisfactory answer (yet? ;()

Sure there are many ways to introduce integers from natural numbers. The map

(boolean sign, natural absValue) -> integer

is even more obvious (although less elegant) than

(natural, natural) -> integer that was mentioned in the Arturo's post. Both have interesting geometric interpretations.

Natural numbers are a ray (half-infinite line), a set of discrete points on a ray to be more presize. In the first construction we take a ray and add its copy rotated 180 deg, that is:

. . . . . . . . . . . >

union

<. . . . . . . . . . .

equals

<. . . . . . . . . . . . . . . . . . . . . . >

In the second construction we take a ray and add its copy rotated 90 deg, so that the cartesian product is a quarter plane, that is

. . . . . . . . . . . >

cartesian product with

^

.
.
.
.
.

equals

^

.  .  .  .  .  .  .
.  .  .  .  .  .  .
.  .  .  .  .  .  .
.  .  .  .  .  .  .
.  .  .  .  .  .  . >

with diagonals as equivalence classes... Received on Tue Oct 24 2006 - 11:04:10 CDT