From: Everett L Williams II <rett@...>
Date: 2010-12-29T21:59:35+09:00
Subject: Re: Numeric comparison with nil - Math masochists only!!

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serialhex wrote:
>>
>>      
>>>        
>> I can't imagine where you got the idea that a nul is less than minus
>> infinity. Mathematically, a null is basically undefined as in dividing by
>> zero. I have no idea what your use of this is, but mathematically you are in
>> the wrong pew.
>>
>> Everett L.(Rett) Williams II
>>
>>
>>      
> where i get that from is this:
>
> when you look at a graph of 1/x lim(+x->0) +infinity; lim(-x->0) -infinity;
> (that's also what i learned in my calculus courses) so 1/0 (kind of) has a
> value depending on which direction you approach 0 from.
>
> null on the other hand - as you said - is undefined.  and when you compare
> null to ANY value - even neg infinity - you still have a value on one hand
> and nothing on the other.  and while it sucks, having -infinity dollars you
> have SOME value (to bill collectors) and having nil dollars you have no
> value (to anyone).  that example is kind of bad cause nil == 0, but that's
> not my point.  if you read some of the papers i provided in the first post
> (esp. this one:
> http://www.tondering.dk/main/index.php/surreal-numbers) part of the
> definition of a surreal number is a comparison with nil.  the first surreal
> number { nil | nil } is defined as 0, and the second generation { { nil |
> nil } | nil } is defined as 1 and { nil | { nil | nil } } is -1 ( commonly
> written simply as { | }; { 0 | } and { | 0 }. and {  0 | 0 } is not
> well-defined in the definition of surreal numbers )
>
> so while it might not make sense to most people (indeed, i'm working on
> stretching my brain around all this) this is the definition i'm working
> with, and i'm not going to argue with math phd's
>
> as for the utility of it all?  surreal numbers are commonly used in game
> theory.  though the reason why i'm building this class is not for utility,
> but as an exercise in 'can i do this?'  there are some problems that may
> come up later i'm going to have to find some way to deal with ( sets of
> infinite objects being one of them, surreal numbers being cool enough that
> it gives meaning to things like infinity + 6 and infinity/2 ).
>
> so i hope i answered your question and maybe taught you something.
>
>    hex
>
> p.s. i still might be mostly wrong, but again, i'm trusting the articles i'm
> reading.  maybe i should have one of those cool math-like people look at
> this?
>
>    

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.

Everett L.(Rett) Williams II


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