Re: Division by zero. Go ahead and laugh.

From: robert j. kolker (nowhere_at_nowhere.net)
Date: 10/09/04 

Date: Fri, 08 Oct 2004 21:14:55 -0400

Lefty wrote:

>>If 1/0 is defined a logical contradiction follows, to wit, 1 = 0. If you
>>like your systems to be consistent then forget about dividing by zero.
>>
>>The only place were dividing by zero makes any sense is in an algebra
>>who only element is 0. Which is kind of useless.
>
>
>
> Precisely.
>
> So what do we do ? We declare it to be "undefined", or "does not exist".

We declare -division by 0- as undefined. 0 itself is a perfectly nice
number and it is special being the identity of the additive group.

Bob Kolker

>
> What is really happening here is some type of disintegration of logical
> consistency at the singularity which is created by attempting to divide 1/0.

There is no inconsistency. If division by 0 is allowed then 1 = 0 which
means everything is equal to 0.

>
> Dont you find this amazing ? I am perplexed by this. I find it really
> incredible. Yes, you can define things so that the whole question just goes
> away. But, if you dare to attack it, there could be something to learn from
> it.

The lesson to be learned is not to permit the rules of the system to
lead to inconsistency. That is not the least bit astounding. It is just
plain good sense.

Bob Kolker

>
>
>

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