Re: Attempts to Refute Cantor's Uncountability Proof?

Hatto von Aquitanien wrote:
Aatu Koskensilta wrote:

Consider permutations of N - that is, bijections from N to N. A simple
cardinality argument shows that not all of them are recursively
enumerable.

I believe you are talking about something different from what I am talking
about. You seem to be talking about a set of bijections, not a specific
bijection.

Indeed I was. The uncountability of the set of bijections from N to N immediately yields the existence of bijections to N that are not recursively enumerable.

Hatto von Aquitanien wrote:
>> N is recursively enumerable. The
definition of recursive enumerability might as well be - and in some
instances is given as - a bijection to N.
That would be silly. Where can one find this definition?

It may be that I need to allow for the domain being a subset of N, but the
general form of recursive definition I am familiar with is:

f(1)=c, f(x')=F(x,f(x)), x element of N.

Where x' is the successor of x.

That's the schema of definition by primitive recursion. It's apparent you just don't know what recursive enumerability means - why not take the time to find out?

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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