Re: Integers and Mathematical Correctness

[csampson@inetworld.net (Charles Sampson)]

chris.danx <chris.danx@ntlworld.com> wrote:

> Hi,
> 
> To most this may seem insignificant but I'm more mathematically minded and I
> just found something out.  Many programming languages don't implement
> division properly!
> 
> For example -3/2 should be -2 not -1, with a remainder 1 not -1.
> 
> I'm trying to implement integer division the "proper" way (according to
> Euclid), just for fun (and to provide a mathematically correct package for
> anyone who gets annoyed by this).

     I'm not sure how you determined that the "proper" definition of 
integer division is to return floor (a/b), where "/" is mathematical 
division.  The definition used by most programming languages preserves 
the very useful property -(a/b) = (-a)/b = a/(-b), where this time "/" 
represents integer division.

     Please explain the Euclid reference.  I don't have any History of 
Mathematics books available, but I don't remember that Euclid had nega-
tive numbers to work with.

                                Charlie