Re: Cantorian pseudomathematics

david petry wrote:
> Han.deBruijn@xxxxxxxxxxxxxx wrote:
>
> > The (best / most common) materialization of the real numbers is the
> > type
> > called floating point / double precision in a modern digital computer.
>
>
> What I have been advocating is that the right way to develop the real
> numbers is to first introduce probabilistic notions into the
> foundations of mathematics, and then develop a notion of
> "finite-precision real number" as a rational number plus an estimate of
> the uncertainty to be attached to the number.  Then real numbers are
> the limiting case of finite precision real numbers as the uncertainty
> goes to zero. The key idea is that a finite precision real number
> includes an estimate of its own uncertainty (imprecision), and thus it
> is not the same as a floating point number.  And note that when we do
> calculations, we must keep track of the uncertainties.  Also note that
> this is not the same as standard constructivism.

If you wish to be taken seriously, then you should develop the real
numbers in the way you are advocating.  If you can do it, it sounds
interesting, although it is not clear to me that it would be taken
seriously in any event, but that is true of much research.  At least
that way you would not be taken as a cheerleader for a team that
someone is just thinking about forming.


Regards,
Achava

.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... > The materialization of the real numbers is the ... > called floating point / double precision in a modern digital computer. ... the uncertainty to be attached to the number. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... numbers is to first introduce probabilistic notions into the foundations of mathematics, and then develop a notion of "finite-precision real number" as a rational number plus an estimate of the uncertainty to be attached to the number. ... Then real numbers are the limiting case of finite precision real numbers as the uncertainty goes to zero. ... The key idea is that a finite precision real number includes an estimate of its own uncertainty, and thus it is not the same as a floating point number. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... numbers is to first introduce probabilistic notions into the foundations of mathematics, and then develop a notion of "finite-precision real number" as a rational number plus an estimate of the uncertainty to be attached to the number. ... Then real numbers are the limiting case of finite precision real numbers as the uncertainty goes to zero. ... The key idea is that a finite precision real number includes an estimate of its own uncertainty, and thus it is not the same as a floating point number. ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... >> called floating point / double precision in a modern digital computer. ... > the uncertainty to be attached to the number. ... > the limiting case of finite precision real numbers as the uncertainty ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... > david petry wrote: ... >> the uncertainty to be attached to the number. ... > numbers in the way you are advocating. ... Now I have nothing to do with the mathematics community, ...
    (sci.math)
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