[NBLUG/talk] The Romans' ban on zero

[mrp]

On Thu, May 29, 2003 at 10:40:48AM -0700, Steve Zimmerman wrote:
> Eric Eisenhart once astutely remarked that the Romans
> banned the numeral "0".  Could this ban have some
> relation to the modern-day mathematical ban on
> division by zero?

The Romans didn't "ban" the numeral 0 any more than they banned cell
phones.  The numeral 0 didn't exist in the roman world.  The arabic
numbering system wasn't is use in europe and wouldn't be for many hundreds
of years after the fall of the Roman empire. (About 1200 A.D. I think)

> I mean, why is division by zero banned, anyway?
> 0 / 0 = 1 and n / 0 = 0, where n != 0.  

0/0 is not 1, and n/0 is not 0. If they're any number they would be
infinity, but it's actually just not defined. (A full discussion as
to why "undefined" is a better answer than infinity is out of the
scope of this newsgroup, but then so is this whole question. Hint: 
consider the function 1/n as n approaches 0, both from the positive
direction, and from the negative direction.)

Some computer architectures have a special numeric value "NAN" which
stands for Not A Number.  This happens when you get an answer that can't
be expressed in the current representation (like x/0, Cotan(0), Tan(Pi),
sqrt(-1) (if the system can't handle imaginary values), overflows,
underflows, etc.)

>                                         Is it not obvious that
> any nonzero real number divided by zero equals zero, because
> zero will go into that number zero times?  

No... it will go in an infinite number of times... think it through.
If I have 5 of something, how many times can I take away no items before
I run out?  The first time, I have 5 items left.  The second time
I have 5 items left.  Third time... you get the picture.

   -- Mitch