Re: On Programs That Output Themselves

Chris Menzel, Charlie-Boo and Martin Shobe wrote:

> >> Your proof applies only to those programing languages
> >> that satisfy your axioms. In order to apply your proof to all
> >> programming languages (which is what you claimed you were
attempting
> >> to do), you would have to show that all programming langauges
satisfy
> >> those axioms. Which means you need to have some definition of a
> >> programming language.
> >
> > A programming language is a mapping from a recursively enumerable
set
> > onto the set of recursive functions.
>
> Any r.e. set? If not, which? This isn't much of a definition.

Yes, any. What's wrong with it?

> > (Because of cardinality, you can't map an aleph-0 set onto an
aleph-1
> > set.
>
> Why do you think this is a relevant qualification in this context?

I'm just making the point that the range is a proper subset of the
aleph-1 set.

> Please be specific. (And why do you seem to be assuming the
continuum
> hypothesis?)

Maybe you're talking about terminology. I call N aleph-0 and R
aleph-1. (Dumb me if that assumes CH.) A map from a set to its
powerset, ok?

C-B

.

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