Re: bijection of R: R <--> Rx.....xR

> Does anyone reject this method on philosophical
> grounds?

the question is how do you define a function. You seem to want it to mean the a function takes a value and by some proccess it manufactures a new value. If you can formalize it further you may have an interesting concept. The usual definition of a function is not like that. A function is just a relation satisfying some relation. Under this definition there is no problem with what was proposed.

> The digits are merely a representation of a real
> number,

you are right, but it is an effective way to define a function.

> not the real number itself. A value (a) and (b) in
> the reals
> would seem more valid, and a function defined
> mathematically:
> c = f ( a, b ).
> This thing you guys are doing is sort of a three tape
> Turing solution.
> Yes it works but where is the purity?
> How about a swirl where
> t = c
> r = c d
> where t is theta and r is radius.
> now a = r cos t
> and b = r sin t
> Within a delta related to d there will be a range of
> c that matches for
> any a and b.
> If more accuracy is needed then drop d.
>
> Does this approach work for 3D?
> I don't see it.
>
> -Tim
>
.

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