Re: Orlow cardinality question

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > Randy Poe said:
> >>
> >>
> >> Tony Orlow (aeo6) wrote:
> >> > So, you can't summarize what it is that cardinality is supposed
> >>
> >> by Tony
> >>
> >> > to accomplish,
> >>
> >> However, the Cantor definition DOES accomplish what it
> >> is supposed by its definer to accomplish, which is
> >> to establish a complete ordering of sets, both finite
> >> and infinite.
> >>
> >> > but claim it is other than determining the size of a set? What is the basic
> >> > purpose of this theory, if not to measure sets?
> >>
> >> See above.
> >>
> >> "Ordering" does not require a notion of "size".
> >>
> >> - Randy
> >>
> >>
> > Well, then, no one should object to my attempts to establish a precise notion
> > of size for infinite sets.
>
> What people have been objecting to is your claim that cardinality
> is inconsistent and "obviously wrong". You have been repeatedly
> told that there are other measures of "size" for sets, and you
> are free to invent your own if you wish, and if others find
> it useful and/or interesting they might adopt it. But if you continue
> claiming that cardinality is inconsistent and "obviously" wrong,
> or claiming that there are infinite naturals, or a largest
> integer, you are going to see objections.
>
> Stephen
>
I never claimed there was a largest integer. Infinite integers? Yes, I claim
there are such things. Do you claim there is an infinite set of distinct finite
naturals? Well, according to both information theory and infinite series that
is impossible. I am entitled to my objections, when Cantorians tell me my
understanding of set size is wrong and theirs is right. If you want a contest,
you lose. Cardinality is woefully inconsistent with the rest of mathematics
when it comes to infinite sets, because many of its assumptions and axioms are
unfounded.
--
Smiles,

Tony
.

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