Re: abundance of irrationals!)


imaginator...@xxxxxxxxxxxxx wrote:

> > Do you really? Where starts infinity?
>
> Huh? "Infinity" doesn't "start" anywhere...

Of course it doesn't because it is nowhere (actually).
>
> > because I don't think
> > > that if I start counting them, that I will ever stop.
> >
> > That s potential infinity.

> > But that is not mant by set heory, because
> > it does not supply a cardinality, in particular it does not lead to
> > aleph_0.

Correct. Nevertheless it is the only coherent notion concerning
infinity.

> > As long as the number of your numbers counted is finite, the
> magnitudes
> > will be finite. If one of them changes, the other will change too
> > simultaneously.
>
> Sounds exotic. You mean that one of my even (finite, normal) integers
> (call it P) is perfectly OK one minute, then it suddenly changes?

No. But people who believe in the existence of actual (or finished)
infinity must believe that.
>
> > > OK, how many of them are infinite?
> >
> > Precisely as many as do not fit into a finite set.
>
> "Do not fit"? Tell me, pray, how many do "fit into a finite set"? Is
> this some particular number, or can I expect some numbers to fit one
> minute, then jump out the next?

No. All finite natural numbers do fit into a finite set (because
natural numbers count themselves teir cardinality). I argue only in
order to show the adherents of actual infinity that their "mathematics"
anyway ...
> Anyway, this is obviously a waste of time.

Regards, WM

.

Relevant Pages

  • Replacing speakers in a Volvo V70 1998
    ... Having replaced the stock head unit, I now want to upgrade the speakers to ... In the past I have always used Infinity Kappa's, and judging by their ... would fit, without the need for extensive housing modifications. ...
    (uk.rec.audio.car)
  • Re: little o notation
    ... supposed to go to zero. ... odoes not fit with my current ... infinity. ... Why does the concept of a decreasing function not make sense ...
    (sci.math)
  • Re: Locked memory
    ... Annie wrote: ... FFFFh was still the highest number ... As, the last time I checked, you could fit "infinity" ...
    (alt.lang.asm)
  • What is the expected value for this function ?
    ... I know the function corresponds to f=1/x ... so one can argue then the expected value is +infinity. ... not fit well to me. ...
    (sci.stat.math)
  • Re: Cantors Argument Skolemized?
    ... separation to carry through Cantor's argument. ... a theorem of ZF - Infinity that for any finite set there is a finite ... i.e., there is not free induction, but, induction out towards infinity ... constructions of the reals see some special functions in the digital. ...
    (sci.logic)