Re: Computable functions/reasls: followup.

On 5 Sep, 05:05, Bill Taylor <w.tay...@xxxxxxxxxxxxxxxxxxxxx> wrote:

OK then, the debate seems to have subsided, so maybe I could make
a summary, and perhaps add a few extra words.

Thank you, very interesting.

So, if we consider our domain as *tame reals*, that is, reals whose
ever-increasingly-accurate rational approximations are known, (as
above),
but also for which it is GIVEN whether or not they are rational,
then we can deal with discontinuous functions happily.

Is this the oracle you mean? That is, you mean that to the oracle is
attached some sort of flag telling in advance "rational" vs.
"irrational"? If so, I'd be interested in understanding how this kind
of information is "encoded", or otherwise how it is exploited by a TM
that is supposed to get that input. (I am not getting the specifics of
that "GIVEN".)

IMHO this would cure the lingering doubts expressed above, though it
would hardly be worth the trouble for evryday math.  But it might be
a satisfying approach for some types of people.

Above all the engineers! :) There is that matter of the exception-free
systems.

-LV
.