On 2010-06-20, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > "Tim Little" <email@example.com> wrote in message >> 1) Recursive enumerability has nothing to do with it. > > So you assert. Personally, I think that the fact that the computable Reals > are not recursively enumerable is intimately related, as a set being > recursively enumerable in this context basically means the same thing as > there being a mapping from N to exactly that set, ie a list of elements.
What you have just said as the definition for "recursively enumerable" is *exactly* equivalent to being a countable set!
I suggest you look up the definition for a recursively enumerable set, and see how it differs from the definition of a countable set.
>> 2) The word you should be using instead of "recursively enumerable" >> is "surjective". > > Well, recursively enumerable is a property of sets, and surjective is a > property of mappings, so dunno what you are talking about.
Did you forget what you wrote? Look again at what you claimed:
"What Cantor proved (in more modern parlance) is that there is no recursively enumerable function from N -> R".
You were the one applying the term "recursively enumerable" to a function. I was merely correcting your mistake.
> Well, that's very rude of you.
Yes, it was. Polite correction of your errors wasn't getting anywhere, and you did not appear to be aware of how bad it looks to be declaiming "Cantor didn't prove that the reals were uncountable!" while obviously not grasping some of the most basic concepts in set theory, proof, and computability.