On 19 Jun., 15:31, stevendaryl3...@yahoo.com (Daryl McCullough( wrote: > Peter Webb says... > > >but because Cantor's proof explicitly constructs the > >anti-diagonal it is clearly computable > > It's a computable function of *two* arguments. That doesn't > mean that there is a computable function of *one* argument.
What a ridiculous discussion!
Whatever Cantor's argument produces, it is something more or less definite. But everything that is definite enough to be distinguished from every other real number belongs to a countabe set. And everything less definite cannot be distinguished from other less definite objects and is certainly not a number.
Cantor's "proof" shows either that a countabke set is uncountable or that a number that can be distinguished from every other number cannot be distinguished from every other number.
It is a pity that you were told that many years ago and have not yet understood it!