Re: infinity

Ross A. Finlayson wrote:
> Virgil wrote:
> > In article <MPG.1d8907213041699698a219@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > I showed that no set of strings up to and including any finite length
> > > can possibly be finite. This applies to ALL finite length strings, so
> > > it applies to ALL the strings in your set of finite strings. What I
> > > showed is that you can ONLY have an infinite set of strings if you
> > > have strings of infinite length, which you don't.
> >
> > If, as TO keeps claiming, the set of all finite strings were truly
> > finite, the concatenation of all those finite strings would still be a
> > finite string, but longer than any string in the *finite* set of *all*
> > finite strings.
>
> Yeah, so what. Ord would be an ordinal.

Who is 'Ord', actually?

> If it's an infinite set, it's infinite.

Right, and if it's a green set, it's green. Similarly for yellow and
pink.

> Ord is order type of ordinals.

> Well-order the reals. Why doesn't that imply adjacent points in the
> normal ordering of the reals?

Because there is not necessarily any relationship between the
well-ordering and the natural ordering. In fact, as is obvious, there
are no adjacent points in the reals, so the "necessarily" can be
deleted without changing the meaning.

I suppose you probably knew that already. Never mind - tell us again:
are infinite sets equivalent?


> You address finitists in your arguments about the infinite? That's
> strange.

You've forgotten your lines, Ross.

Brian Chandler
http://imaginatorium.org

.

Relevant Pages

  • Re: Is continuum completely filled up?
    ... cannot identify adjacent reals generated by the construction, ... After all, the integers are likewise an infinite set, but there is ... strings in this context, since a finite-length bit string can be ... the sum is one thing, and then argue that it is another. ...
    (sci.math)
  • Re: Infinite Binary Strings: A Question
    ... strings to exist in the same list, and whether 'unpredictable' is a good ... description of this aperiodicity is not crucial. ... well known argument that the power set of an infinite set 'exceeds' the ... argument about infinite binary strings)? ...
    (sci.math)
  • Re: Infinite Binary Strings: A Question
    ... strings to exist in the same list, and whether 'unpredictable' is a good ... description of this aperiodicity is not crucial. ... well known argument that the power set of an infinite set 'exceeds' the ... argument about infinite binary strings)? ...
    (sci.math)
  • Re: Infinite Binary Strings: A Question
    ... strings to exist in the same list, and whether 'unpredictable' is a good ... description of this aperiodicity is not crucial. ... well known argument that the power set of an infinite set 'exceeds' the ... argument about infinite binary strings)? ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... infinite set has the quality that there are proper sets of it (that are not ... > in the set of strings that correspond to octal representations of integers ... integer along the way there will be strings in the set of octals that are ...
    (sci.cognitive)
Loading