From: Phillip Gawlowski <cmdjackryan@...>
Date: 2010-11-26T04:10:15+09:00
Subject: Re: Ruby 1.8 vs 1.9

On Thu, Nov 25, 2010 at 7:43 PM, Yuri Tzara <yuri.tzara@gmail.com> wrote:
> Phillip Gawlowski wrote in post #963922:
>> I'm quite aware that IEEE 754 defines the result of x_0/0 as
>> infinity. That is not, however, correct *in a mathematical sense*.
>
> Yes, it is. The creationist analogy continues, I see. Even when given
> facts which refute his position a second and third time, Mr. Gawlowski
> continues to ignore them while simply repeating his opinion.
>
> He twice ignored my suggestion to look up one-point
> compactifications. He twice ignored my explanation of joining oo to a
> line to make a circle, and of joining oo to a plane to make a
> sphere. He also ignored the same information found in the link
> provided by Adam.
>
> It's not coincidence that the IEEE operations on oo match the rules
> for the real projective line.
>
> http://en.wikipedia.org/wiki/Real_projective_line#Arithmetic_operations
>
> The only exception is the result of oo + oo, however in computing it
> is convenient for that to be oo rather than undefined. Of course
> there's the +/- distinction for oo (also convenient in computing)
> which is eliminated by identifying +oo with -oo, as one would expect
> for a circle. There are perhaps other technicalities but generally
> IEEE operations are modeled after the real projective line. This is
> useful.

Quote Wikipedia:
"Unlike most mathematical models of the intuitive concept of 'number',
this structure allows division by zero [snip formula], for nonzero a.
This structure, however, is not a field, and *division does not retain
its original algebraic meaning in it*."

Emphasis mine. Your argument is also called "moving the goal posts".
But even if we consider it: non-algebraic systems are not something
99% of all non-professional-mathematicians engage in (so, we can toss
in a "no true Scotsman" fallacy into the bargain).


-- 
Phillip Gawlowski

Though the folk I have met,
(Ah, how soon!) they forget
When I've moved on to some other place,
There may be one or two,
When I've played and passed through,
Who'll remember my song or my face.