[NBLUG/talk] The Romans' ban on zero

[Eric Eisenhart]

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?

Heh.  No, it was because zero was used on the docks by Arabic-speaking
traders that could count groups of things so much faster than Romans that it
gave them a trading advantage.  ("Okay, so I've got 18 boxes with 10 things
in each and a box with 2 things in it, meaning I have 180 things in the full
boxes, and 182 total" vs "Okay, so I've got XIIX boxes with X things in each
and a box with II, so you carry the V and uhm..." (eventually reaching
CXIIXC or CXXCII or whatever)

> I mean, why is division by zero banned, anyway?
> 0 / 0 = 1 and n / 0 = 0, where n != 0.  Is it not obvious that
> any nonzero real number divided by zero equals zero, because
> zero will go into that number zero times?  

You've got it backwards.

1/1 = 1
1/0.1 = 10
1/0.01 = 100
1/0.001 = 1000
So 1/0 = infinity.

Zero will go into a number an infinite number of times, because it's so
small.  If you have a whole pie of circumference P and you give away a slice
of P/4 arc length, you can give away 4 of those.  On the other hand, you can
give away an infinite amount of no pie.
-- 
Eric Eisenhart
NBLUG Co-Founder & Vice-President Pro Tempore
The North Bay Linux Users Group
http://nblug.org/
eric at nblug.org, IRC: Freiheit at freenode, AIM: falschfreiheit, ICQ: 48217244