[gambit-list] (Slightly) Off topic: Sample Scheme code for the computable reals

John Cowan cowan at ccil.org
Tue Feb 1 17:41:21 EST 2022


This is a truly great paper, and I am glad to have read it.  But there is
something wrong with the theorem at the beginning of 4.14 ("all computable
functions that are defined for all computable real arguments and return
computable real results are continuous"), probably that the claim is
over-generalized (or maybe just that I am a high-school mathematician).
The domain of the signum function obviously includes the computable reals.
The codomain is {0, 1, -1}, which are all computable.  Yet signum is not
continuous at 0.  This can be generalized to other stepwise functions with
any countable number of discontinuous points.  What gives?


On Tue, Feb 1, 2022 at 12:15 PM Bradley Lucier <lucier at math.purdue.edu>
wrote:

> I wrote a paper on the computable reals with a page of (Gambit) Scheme
> code at the end that implements some of the examples.  The code was
> organized for clarity of presentation (base 10, easiest algorithms,
> etc.), so it's not production quality, but there are references for
> people who are interested:
>
> https://scholarship.claremont.edu/jhm/vol12/iss1/25/
>
> I made sure that the typesetting didn't screw up the code, that you can
> just copy it to a Gambit REPL and everything works.
>
> And Section 3 tells a funny story about me learning how to compute
> square roots by hand.  (Perhaps only a mathematician could write that
> sentence!)
>
> Brad
>
> _______________________________________________
> Gambit-list mailing list
> Gambit-list at iro.umontreal.ca
> https://mailman.iro.umontreal.ca/cgi-bin/mailman/listinfo/gambit-list
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.iro.umontreal.ca/pipermail/gambit-list/attachments/20220201/777328be/attachment.htm>


More information about the Gambit-list mailing list