Re: Well Ordering the Reals

David R Tribble said:
> David R Tribble said:
> >> 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?
> >
>
> Tony Orlow wrote:
> >> Yes, I have tried to use examples like
> >> 2x+3y-5z=9
> >> 4x-5y+7z=14
> >> so what are x, y and z?
> >
>
> William Hughes wrote:
> > You have missed the point entirely. The problem is that you say something
> > like "the number is 12.5 x". When you are asked is 12.5 x equal to 12.5 y
> > you say something like "I don't know until you have specified x and y".
> > In response to the comment "12.5 x does not specify a number" you say
> > that all you need is the value of x.
> >
> > You notation is incomplete. Given a "number" in your notation
> > you cannot tell what this "number" is without more information.
> > Nor have you demonstrated that this incomplete notation
> > is useful.
>
> Indeed. Tony, I have two numbers:
> a = 0:111...110
> and
> b = 0:111...110
> but a is not equal to b. Which one is larger?
>
>
The one with the larger limit point. What are your limit points? How many bits
ya got in each? This should concern you.
--
Smiles,

Tony
http://www.people.cornell.edu/pages/aeo6/WellOrder/
.

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