% is not an operator [was Re: Verbose and flexible args and kwargs syntax]

[Eelco]

On 14 dec, 13:22, Jussi Piitulainen <jpiit... at ling.helsinki.fi> wrote:
> > > Is someone saying that _division_ is not defined because -42 div
> > > -5 is somehow both 9 and 8? Hm, yes, I see that someone might. The
> > > two operations, div and rem, need to be defined together.
>
> > > (There is no way to make remainder a bijection. You mean it is not
> > > a function if it is looked at in a particular way.)
>
> > Surjection is the word you are looking for
>
> Um, no, I mean function. The allegedly alleged problem is that there
> may be two (or more) different values for f(x,y), which makes f not a
> _function_ (and the notation f(x,y) maybe inappropriate).
>
> Surjectivity is as much beside the point as bijectivity, but I think
> we have surjectivity for rem: Z * Z -> Z if we use a definition that
> produces both positive and negative remainders, or rem: Z * Z -> N if
> we have non-negative remainders (and include 0 in N, which is another
> bone of contention). We may or may not want to exclude 0 as the
> modulus, or divisor if you like. It is at least a special case.
>
> It's injectivity that fails: 9 % 4 == 6 % 5 == 3 % 2, while Python
> quite sensibly has (9, 4) != (6, 5) != (3, 2). (How I love the
> chaining of the comparisons.)

My reply was more to the statement you quoted than to yours; sorry for
the confusion. Yes, we have surjectivity and not injectivity, thats
all I was trying to say.


> > That is, if one buys the philosophy of modernists like bourbaki in
> > believing there is much to be gained by such pedantry.
>
> I think something is gained. Not sure I would call it philosophy.

Agreed; its more the notion that one stands to gain much real
knowledge by writing volumnius books about these matters that irks me,
but I guess thats more a matter of taste than philosophy.