On 23/06/06, Brian Hulley <[EMAIL PROTECTED]> wrote:
> This equation is just a shortcut, so I can't see how can it be
> ill-typed. It means something like: if you add one element to an
> infinite list, will it be longer?
What does your intuition say about this?
It won't be longer. How can it be? It's already infinite ;) It's like
throwing things into bottomless hole and expecting it to get more
"full."
But this explanation might just be vapid sophistry. Do you *really* want to
trust it?
I perceive it as a way to explain to beginner students where bijection
idea comes from. It's all it means to me. I suppose the whole idea is
to start at something intuitive and then extend it to completely
counter-intuitive notion of being infinite.
Just that there is a conflict with intuition no matter which option you
choose: if I think that the list would be longer, I have to reject any proof
to the contrary, but then my intuitions about valid proof are confounded,
whereas if I accept the proof, my intuition about physical objects is
confounded: if the list doesn't get longer, then where *is* the thing I
added to it? Did it just disappear?
So for these reasons I find that infinity is a troublesome concept.
I suppose infinity can't be totally intuitive in the end. We are not
used to handle infinite objects and intuition as such was not
developed to handle them.
Regards,
Piotr Kalinowski
--
Intelligence is like a river: the deeper it is, the less noise it makes
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
