On 19/09/2011 07:26 PM, Kevin Wampler wrote:
> On 9/19/2011 11:20 AM, Orchid XP v8 wrote:
>>
>> Well, if you define it to be Heth then it's defined... It's not
>> necessarily a good idea though.
>>
>> Fact is, 0 * infinity = 0, so it's not a sensible answer. Unless you
>> change the axioms of arithmetic. (And even if you do, division by zero
>> leads to logical paradoxes left, right and center...)
>>
>
> Somehow I knew you'd post something like this. The fact is, however,
> that defining division by zero to be infinity is actually quite common
> and very useful in some areas of mathematics, and it doesn't lead to
> paradoxes if you modify arithmetic suitably.

Well, sure. I mean, if you "modify arithmetic" such that "zero" actually 
means one, then division by zero becomes /perfectly/ sensible...

In practise, I've seen people talk about a result "approaching 
infinity", or about infinity being the limit of something. And I've seen 
either the real line or the complex plane extended to include a "point 
at infinity". But I've never seen anybody attempt to claim that dividing 
by zero yields a definite, reliable "answer". (Other than engineers, who 
are of course wrong.)

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