On Wed, Dec 29, 2010 at 1:59 PM, Everett L Williams II
<rett / classicnet.net> wrote:

> I haven't the time nor energy to get through all of that, but I can clearly
> state that your explication of division by Zero is just wrong. Undefined is
> just that...undefined. You can approach by any means that you wish, but it
> does not change the nature of the beast. You might note that, as much as
> physicists and cosmologists deal with very, very large numbers, they still
> dislike infitities in equations, because they often lead to mathematical and
> sometime physical black holes. All computer logic is finite and
> deterministic, so you may model infinities on a computer, as metadata, but
> you cannot do any calculation that includes them.

Why? Sciences are irrelevant in formalisms.

You can indeed do some calculations, the fact that there are infinite
natural numbers does not mean you can't add some of them in a
computer. Certainly not all of them, but some.

In that sense arithmetic with infinite quantities is no different. You
can represent infinites or infinitessimals just fine and define
operators on them, just the way you do with natural numbers. In a
computer you are always modelling, you also model N.

It is common that formalisms in Set Theory start with the empty set,
because the axioms give you that one. That's serialhex's nil in
Conway's classic book on the subject. That's how the naturals are
modelled in Set Theory also, is 0, {} is 1, and n = n  {n}. You
only have the empty set and operations like union or the power set to
build upon.