Re: infinity

stephen@xxxxxxxxxx wrote:
> albstorz@xxxxxx wrote:
> > Torkel Franzen wrote:
> >> albstorz@xxxxxx writes:
> >>
> >> > But infinite many numbers. Who has a method to distinguish what can be
> >> > infinite and what not?
> >>
> >> Why are you still stumbling about in a Cantorian fog? Just think
> >> about what "infinite" means!
>
>
> > Let's have a little help by Achilles. He starts from his house. Every
> > step he does withdraws him one meter more from his house.
> > He does infinite many steps. But he stays always in a finite distance
> > to his home. So he will easily comes back to the lunch, the turtle
> > prepared.
>
> > Achilles does infinite many steps as there are infinite many numerals
> > in the infinite set, but he stays always in an finite distance, since
> > no number in the infinite set will become infinite.
>
> So you are saying that Achilles keeps taking steps and never,
> ever stops. That is what 'infinitely many steps' means.
> Then after he never ever stops, he stops and returns
> in a finite amount of time.


Math considerations work outside of time, space and matter.

If you take the time in consideration which is needed by a process,
especially the computing time, then you are not able to do pure math.
The infinite set of numerals is build by infinite many numbers or
infinite many steps, but "exists" at once.
If you insist real: "Infinity means never, ever ending", what should be
an infinite, a never ending set? Every mathematician is only able to
work with the part of the set which just now exists? Then every set we
use could only be finite.
You can imagine the story by thinking, every step which Achilles do
needs just half the time the step bevor had needed. So Achilles will be
at home in finite time in spite of doing infinite many steps.


>
> Is that really your concept of infinity?


What is your concept?


>
> > One word, two concepts.
> > That's the way I think about infinity.
> > For you, may be, it is fog. For me it is clearness.
>
> I do not see anything clear in talking about someone
> who keeps taking steps and never stops, but who also stops.
> Doesn't the contradiction between 'never stops'
> and 'stops' bother you?
>
> Stephen


There is no contradiction. Only the contradiction whitch occures by
applying standard math definition of infinity. And I assume that this
seems to you not to be a contradiction.

Regards
AS

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