On Thu, Nov 25, 2010 at 9:19 PM, Yuri Tzara <yuri.tzara / gmail.com> wrote:
> Phillip, regarding defining 1/0 you said,
>
>> It cannot be infinity. It does, quite literally not compute. There's
>> no room for interpretation, it's a fact of (mathematical) life that
>> something divided by nothing has an undefined result. It doesn't
>> matter if it's 0, 0.0, or -0.0. Undefined is undefined.
>
> Nonsense. These claims are roundly refuted by

Actually, they aren't I said for "x_0/0 the result is undefined", and
the Extended Real number has the caveat that x_0 must be != 0.

>> I'm quite aware that IEEE 754 defines the result of x_0/0 as
>> infinity.  ¨Βθαισ ξοτ¬ θοχεφες¬ γοςςεγͺινατθενατιγαμ σεξσεͺ>
> Nonsense. Infinity defined this way has solid mathematical meaning and
> is established on a firm foundation, described in the link above.

A firm foundation that is not used in algebraic math.

>> The IEEE standard, however, does *not* define how mathematics work.
>> Mathematics does that. In math, x_0/0 is *undefined*. It is not
>> infinity...
>
> Right, IEEE does not define how mathematics works. IEEE took the
> mathematical definition and properties of infinity and incorporated it
> into the standard. Clearly, you were unaware of this and repeatedly
> ignored the information offered to you about it.

It took *a* definition and *a* set of properties. If we are splitting
hairs, let's do it properly, at least.

>> 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.
>
> That sentence. You evidently do not understand what it means. It does
> not mean what you think it means.

You do know what algebra is, yes?

>> Your argument is also called "moving the goal posts".  ¨Βυτ εφεξ ιζ
>> 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).
>
> Nonsense. Every person who has obtained a result of +oo or -oo from a
> floating point calculation has engaged in it. A result of +oo or -oo
> is often a meaningful answer and not an error. And even when it is an
> error, it gives us information on what went wrong (and which direction
> it went wrong in). It's entertainingly ironic that you attribute
> "moving the goalposts" and the no true Scotsman fallacy to the wrong
> person in this conversation.

Pal, in algebraic maths, division by zero is undefined. End of story.
We are talking about algebraic math here (or we can extend this to
include complex numbers, which IEEE 754 doesn't deal with, either),
and not special areas of maths that aren't used in outside of research
papers. Not to mention that I established the set of Irrational
numbers as the upper bound quite early on.

The and your argument "if you use floats on a computer you use a
non-algebraic system, therefore you use a non-algebraic system when
using a computer" is circular.

The result of x_0/0.0 = infinity is as meaningful as "0/0 = NaN". Any
feedback by a computer system is meaningful (by definition), and can
be used to act on this output:

result = "Error: Division by zero" if a / 0.0 == Infinity

Done.

> Thanks for another great demonstration of the Dunning-Kruger effect.

Ah, the irony.

-- 
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.