On 22/06/06, Brian Hulley
This doesn't mean that these contradictions reflect reality - just that maths hasn't yet reached a true understanding of reality imho.
Well, I for instance believe that contradiction IS the true nature of reality... ;)
For example, why do people accept that infinity == infinity + 1 ? Surely this expression is just ill-typed. infinity can't be a number.
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? I found the explanation in terms of defining bijection between both lists very appealing (along with a "metaphor" of taking one element at a time from both lists and never being left with one of the lists empty, which was demonstrated here as well). Seems I don't understand your problem with infinity after all :) Regards, Piotr Kalinowski -- Intelligence is like a river: the deeper it is, the less noise it makes