In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> That is the point. The argument is trivially wrong, but so famaous > that you cant't believe what you must conclude.
There is something (a considerable amount) wrong with WM but not with either the first or the second of Cantor's uncountability of the reals arguments.
When one goes strictly by the formal definitions of countable and uncountable, Cantor make sense and WM does not.
If one does not go by those definitions, there is no point in talking about countability at all.
Apparently WM has never learned those definitions because he always avoids using them.
So here they are again:
Countable set From Wikipedia, the free encyclopedia
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor. The elements of a countable set can be counted one at a timealthough the counting may never finish, every element of the set will eventually be associated with a natural number. Some authors use countable set to mean a set with the same cardinality as the set of natural numbers. The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable. To resolve this ambiguity, the term at most countable is sometimes used for the former notion, and countably infinite for the latter. The term denumerable can also be used to mean countably infinite, or countable, in contrast with the term nondenumerable. --