On 14 dec, 13:22, Jussi Piitulainen <jpiit...@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. -- http://mail.python.org/mailman/listinfo/python-list
