On Tue, 22 Feb 2005, Michael Neumann wrote:

> 100% agree. I especially cannot understand (at least mathematically) why 
> 0 would be empty and 1 not.

In Cantor-style Set Theory, the Naturals usually get redefined in such a
way that 0 is equal to the empty set. Which means, incidentally, that 0
_is_ the empty set, and vice versa.

That definition is quite popular in Logic, but fails to draw much usage in
the rest of Mathematics. It's not the only definition either. Dedekind's
definition implies 0 is the set of all rationals lower than 0. Those
multiple defs can be thought of as different implementations, while the
usually-used interface consists of the operators +,-,*,/,etc.

In computer science, the first definition would be the most accepted of
the two, simply because the latter involves Real Numbers, which don't
exist in reality, by SkŲžem's Paradox. This may exclude the many lost
souls who don't get math, such Niklaus Wirth, who gave the name of Real to
a floating-point type (!!!) in PASCAL.

(If you think some programmers have bad naming skills when it comes to
writing their programs, find who called the Real Numbers "Real", when
almost all elements of that set don't exist.)

_____________________________________________________________________
Mathieu Bouchard -=- Montr٬l QC Canada -=- http://artengine.ca/matju