you've got to take you're math cap off, and put your cs cap on.
the motivation for defining MOD and DIV is so you can do somethign
like this
row = size DIV columns
col = size MOD columns
the pseudo-mathematics is applied ex post facto. clearly you have to
get a single value out of the operation but that value is never going to
be a member of Z. it's going to be a n-bit binary integer. also,
; cat > /tmp/fu.c
int main(void){
int x;
x = 1 % 0;
}
/tmp/fu.c: In function `main':
/tmp/fu.c:4: warning: division by zero
- erik
Dan Cross <[EMAIL PROTECTED]> writes
|
| On Thu, Dec 15, 2005 at 11:51:15PM -0500, Dan Cross wrote:
| > On Thu, Dec 15, 2005 at 08:04:02PM -0800, Jack Johnson wrote:
| > > So, what *is* -5 MOD 3?
| >
| > Well, in general, it depends.
| >
| > Do you care whether the result a set or an integer? The definitions due
| > to Wirth et al are the former, while the MS definition appears to be the
| > latter.
|
| Hmm, I guess on further reflection I ought to explain what I mean by
| this before someone jumps all over me.
|
| The definition as per Wirth et al gives you a positive generator for an
| equivalence class on Z, whereas the microsoft definition gives you the
| definition of the division function extended to all of Z, which yields
| an integer; the former definition is probably more comfortable for a
| mathematician, and more what one would expect. The latter is more
| comfortable for someone who just wants to write a program. In neither
| case does this have much to do with the actual implementation (that is
| to say, it's not like DIV actually gives you back an object
| representing the set of all integers congruent to 0 modulo some integer
| in Pascal), but only how that language interprets the definitions.
|
| > Regardless, all these definitions are problematic. No where does it say
| > they're defined only on Z*; what if Y is 0?
|
| This is still a problem. You really want a function f: Z x Z* -> Z,
| not f: Z x Z -> Z; that is, for f(x, y) = x div y, y should be non-zero.
| Otherwise, it would be an absurdity.
|
| - Dan C.
