Re: Well Ordering the Reals


Tony Orlow wrote:
> David R Tribble said:
> > William Hughes wrote:
> > > OK, so given
> > > 0:0...010...0
> > >
> > > I have no idea what this means until I have a lot more information
> >
> > Which makes it pretty obvious that Tony's notation is vastly
> > incomplete. If we can't use it to represent a number in no
> > uncertain terms, what good is it? If we always have to explain
> > parenthetically how the sizes and digit positions for each number
> > are different than those of all the other numbers we write, what
> > good is the notation?
> >
> >
> If I can't get a good answer to 3.4*+13-, then what good is arithmetic?


Bad example. Ask rather: what is 12.5 *x + 16.7*y ?
You certainly cannot answer this without knowing what x and y are.
Nor does it help much to say, all you need to know to know
the value of 12.5*x is the value of x.

-William Hughes


Be
> serious. If you can't specify what number you are talking about, how do you
> expect to get any exact results? Oh yeah, you don't. If it's countable, it's
> aleph_0. How interesting!
> --
> Smiles,
>
> Tony
> http://www.people.cornell.edu/pages/aeo6/WellOrder/

.

Relevant Pages

  • Re: Well Ordering the Reals
    ... > Tony Orlow wrote: ... >> William Hughes said: ... Given a "number" in your notation ... > (sum over the TO-naturals x) g2^x ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... David R Tribble said: ... > William Hughes wrote: ... > Which makes it pretty obvious that Tony's notation is vastly ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... > David R Tribble said: ... >> William Hughes wrote: ... >> Which makes it pretty obvious that Tony's notation is vastly ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... Tony Orlow wrote: ... David R Tribble said: ... >> though that's pretty much the definition of an infinite number: ... So then your notation doesn't handle set-theoretic numbers? ...
    (sci.math)
  • Re: infinity
    ... > Tony Orlow wrote: ... >> Randy Poe said: ... I'm not talking for the moment about this notation. ... member of the set of naturals starting at 0. ...
    (sci.math)