On 2006-06-22 at 15:45BST "Brian Hulley" wrote: > Jon Fairbairn wrote: > > infinity+1 = infinity > > Surely this is just a mathematical convention, not reality! :-)
I'm not sure how to answer that. The only equality worth talking about on numbers (and lists) is the mathematical one, and it's a mathematical truth, not a convention. > >> I don't see why induction can't just be applied infinitely > >> to prove this. > > > > because (ordinary) induction won't go that far. > > I wonder why? > For any finite list yq, |y| == |yq| + 1 > So considering any member yq (and corresponding y) of the set of all finite > lists, |y| == |yq| + 1 But the infinite lists /aren't/ members of that set. For infinite lists the arithmetic is different. |y| == |yq| +1 == |yq| If you don't use the appropriate arithmetic, your logic will eventually blow up. > Couldn't an infinite list just be regarded as the maximum element of the > (infinite) set of all finite lists? It can be, but that doesn't get it into the set. -- Jón Fairbairn Jon.Fairbairn at cl.cam.ac.uk _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe