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Xavier Noria wrote:
> 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}. You
> only have the empty set and operations like union or the power set to
> build upon.
>    
You are confusing computer logic and meta-data manipulation. No computer 
can natively deal with the representation of, much less the calculation 
of anything that involves infinity, either negative or positive. You 
certainly can define a set of rules and attempt to create a program that 
models those rules, but you cannot naatively do any such calculation. 
Computers are, by definition, finitie and deterministic, and there is 
not room here to explain exactly what that means, but there is plenty of 
information spread all over the internet on the subject. Let me take a 
small stab at an example. Given to finitie numbers whose sum is within 
the capacity of the instructions of a computer, I can add those two 
numbers and get a third number. Anything beyond that is modeled and 
entirely dependent on my logic rather than the logic of the computer. 
So, you can declare that infinity plus 6 has meaning and you can declare 
what that meaning is, providing a routine that will decode your 
expression of infinity and then follow your instructions for creating 
whatever you have defined as infinity plus 6, but there is no native 
instruction, even in floating point, that can impinge on the correctness 
or the calculation of the answer. It is entirely dependent on the 
meta-logic and meta-data that you have provided. Even extended precision 
math libraries can break a large number down into segments and then use 
the native facilities of the computer in a logically and mathematically 
valid process that leads to arithmetically correct answers, but infinity 
cannot be represented in any nat8ive form within a computer.

If you look up infinity on the wiki, you will find pages upon pages of 
various means of manipulating infinities, and yours may be the latest. 
When I have the time and energy, I will look, but it is hard to get 
excited about the umpty-unth attempt.

Everett L.(Rett) Williams II

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