Re: Infinity =/= Infinity


David R Tribble wrote:
> David R Tribble wrote:
> >> The fact that a set has the property of being infinite (i.e., it
> >> contains an infinite number of elements), does not say anything about
> >> the properties of the elements within the set themselves.
>
> Albrecht Storz wrote:
> >> In same cases yes, in some cases no.
>
> David R Tribble wrote:
> >> Which is the same as saying they are independent properties.
>
> Albrecht Storz wrote:
> > NO. There are two cases. First, there are sets which are conected with
> > their elements like the set of the natural numbers. This sets (every
> > set of all elements of a series) are indexed by the elements or the
> > indices of the elements.
>
> Sets don't have indexes. Elements of sets don't have positions within
> the set. A set is simply a collection of things, like a bag of colored
> marbles. An element does not have a "position" or "index" where it is
> "at" in the set.

Please read befor answer. I talk about sets of elements of series or
sequences.

>
> An "ordered set" is a collection of things that have an ordering
> relation among themselves. That is, each element can be ordered with
> respect to any other element. This allows the set to have a "least"
> member or a "greatest" member (or possibly neither). But this
> ordering does not equate to any kind of "position" or "index" within
> the set.

In this sense I talked about ordered sets.

Regards
AS

.

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