Re: infinity ...


William Hughes wrote:
> albst...@xxxxxx wrote:
> > David R Tribble wrote:
> >
> > >
> > > Because I can prove it (and it's a very old proof). A powerset of
> > > a nonempty set contains more elements that the set. Can you prove
> > > otherwise?
> >
> > This argument is stupid. Is there any magic in the powerfunction? A
> > hidden megabooster for transcendental overflow? What is the very
> > special aspect of the powerfunction to be so magic?
> > Why should all operations with transfinite numbers lead to results with
> > the same "level" of infinity, but only powerfunction beams up to the
> > next level?
> > Is not true: a^2 = a*a? 2a = a+a?
>
> Yes, but the powerfunction does not look like a^2 but 2^a.
>
> > Is the powerfunction something other than a very shortcut for multiple
> > additions?
>
> Yes. You cannot represent 2^x as multiple additions.


Since we talk about x e {1,2,3,4,5,...}, why not?


>
> > Which amount you are able to reach with powerfunction which is
> > unreachable by succesor operation?
>
> Infinity for one. You cannot get from a finite quantity to
> an infinite quantity by using the successor operation (unless
> like TO you are willing to wave a circular magic wand and apply
> the successor operation an infinite number of times).


But with 2^n you will reach infinity? Than you also will reach it with
1+1+1+1+...


>
> >
> > I'm very sensible about this because this argument is found in very
> > much books although it's total meaningless.
> >
>
> I suspect that you mean "sensitive" not "sensible".


Of course.


>
>
> > (Weak minds might be impressed by the big numbers which are easily
> > produced by powerfunction.)
>
> Strong minds are impressed with the fact that there is no
> bijection between X and P(X).
>
> >
> >
> > What in finity holds may not (or do not) hold in infinity.
>
> Words to live by. Start by noting that a finite set has a
> "number of elements" that can be described by a natural number
> while an infinite set (e.g. the set of natural numbers) does
> not have a "number of elements" that can be described by a
> natural number. However, some things are true for both
> finite and infinite sets. e.g. the fact that there is no
> bijection between X and P(X).
>
> -William Hughes


No.


Regards
AS

.

Relevant Pages

  • Re: infinity ...
    ... Is there any magic in the powerfunction? ... > the successor operation an infinite number of times). ... > bijection between X and P. ...
    (sci.math)
  • Re: infinity ...
    ... Is there any magic in the powerfunction? ... the successor operation an infinite number of times). ... bijection between X and P. ...
    (sci.math)
  • Re: infinity ...
    ... > define an infinite number of finite naturals. ... > Tony believes that the successor operation somehow produces infinite ...
    (sci.math)
  • Re: infinity
    ... each member is defined by the successor operation. ... >>> defined as the collection of members which obey these axioms. ... > Tony Orlow wrote: ... >> As all infinite sets are defined by the properties of their elements. ...
    (sci.math)