Re: Orlow cardinality question

stephen@xxxxxxxxxx said:
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> > Randy Poe said:
> >>
> >>
> >> Tony Orlow (aeo6) wrote:
> >> > Randy Poe said:
> >> > > Again, you are insisting on an axiom that doesn't exist,
> >> > > in this case that if A < B, then |A| < |B|. That is, if
> >> > > A is a proper subset of B, then the cardinality of A is
> >> > > smaller than the cardinality of B. As you have been told
> >> > > many times, there is no such requirement on infinite sets,
> >> > > and indeed a property of infinite sets is that there
> >> > > exists A < B with |A| = |B|.
> >> > Cardinality purports to describe the sizes of infinite sets.
> >>
> >> Bzzzzt. Wrong from the starting gate.
> >>
> >> Cardinality purports to be a method to assign an ordering
> >> to infinite sets. This it does remarkably well.
> > An ordering in terms of what? Element values? Standard deviation? No. It
> > purports to be a way of comparing the sizes of sets, that is, it purports to
> > distinguish between a few different infinite numbers of elements, and to prove
> > that no other distinction can be made, which is wrong.
>
> > Try defining the word cardinality in five words or less.
>
> That would be silly. It has a precise mathematical definition.
> Using anything other than the precise mathematical definition
> is pointless, unless you just want to make vague hand wavy
> arguments.
>
> Stephen
>
So, you can't summarize what it is that cardinality is supposed to accomplish,
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?
--
Smiles,

Tony
.

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