There are so many responses, that I do not know where to start.. I'm top-posting since that seems best here, let me know if there are group guidelines against that.
Some clarifications in order on my original post: a. I ASSUMED that '()' refers to tuples, where we have atleast a pair. This is from my Haskell ignorance, so let us forget that for now. b. Also, when I said: tuples can not be ordered, let alone be enum'd - I meant: there is no reasonable way of ordering tuples, let alone enum them. That does not mean we can't define them: 1. (a,b) > (c,d) if a>c 2. (a,b) > (c,d) if b>d 3. (a,b) > (c,d) if a^2 + b^2 > c^2 + d^2 4. (a,b) > (c,d) if a*b > c*d If we can imagine (a,b) as a point in the xy plane, (1) defines ordering based on which point is "more to the right of y axis", (2) based on "which point is more above x axis", (3) on "which point is farther from origin" and (4) on "which rectangle made of origin and the point as diagonally opposite vertices has more area". Which of these is a reasonable definition? The set of complex numbers do not have a "default" ordering, due to this very issue. For enumerating them, we *can* go along the diagonal as suggested. But why that and not something else? By the way - enumerating them along the diagonal introduces a new ordering between tuples. When we do not have a "reasonable" way of ordering, I'd argue to not have anything at all - let the user decide based on his/her application of the tuple. As a side note, the cardinality of rational numbers is the same as those of integers - so both are "equally" infinite. Regards, Karthick On Fri, Mar 4, 2011 at 8:42 AM, Daniel Fischer <daniel.is.fisc...@googlemail.com> wrote: > On Friday 04 March 2011 03:24:34, Markus wrote: >> What about having the order by diagonals, like: >> >> 0 1 3 >> 2 4 >> 5 >> >> and have none of the pair be bounded? >> > > I tacitly assumed product order (lexicographic order). > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe > _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe