Re: Orlow cardinality question

Virgil said:
> In article <MPG.1d20ca236aac34cc989e49@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
>
> > Virgil said:
>
> > > Such vagueness is mathematically unsatisfactory. For finite sets,
> > > bijectability with a standard set can be used to define the "number" of
> > > members in an arbitrary finite set. Such standard sets are commonly
> > > taken to be initial sequences (a set of all elements before or up to
> > > some member of the sequence) of, for decimal numbers, either the
> > > ordered set {0,1,2,3,...} or the ordered set {1,2,3,...}, either of
> > > which can be defined inductively so that they consist of only finitely
> > > long strings of digits..
> > >
> > > If one takes {0,1,2,3,...} as the reference sequence then the initial
> > > sequence is the set of all elememnts before the given element.
> > >
> > > If one takes {1,2,3,...} as the reference, then the initial sequence is
> > > the set of all elements up to and including the given element, with the
> > > empty set as a special case.
> > >
> > > In either case, one then takes the element in question as the "number"
> > > of objects in the set in question based upon a bijection.
> >
> > That's very interestingly stated, given your repeated objections to my
> > statement that a set of naturals beginning with 1 always has the set size as
> > its maximal element,
>
> Which need not be the case, as in the first example above. But in any
> case, it is the sets which exist first and the numbers, as
> representations of the cardinality of those sets, which are derived from
> the sets,
"beginning with 1" Learn to read.
In this case the sets are defined uniquely by the natural number. Sorry.
>
>
> >
> > I have talked about the two unit infinities
>
> Is that anything like finite infinities?
Finite numbers are infinite relative to infinitesimal numbers, so sure, despite
the fact that it sounds funny to you. Have a nice snicker.
>
>
> > > Induction only describes what is true for MEMBERS of the set of all
> > > naturals, it says nothing about the set itself.
> > It is true that, for every n in N, the set of naturals from 1 to n has n as a
> > maximal element and also as a set size.
>
> As a representative of set size.
>
> Meaning that there is a standard set, sometimes named by its last
> element, which is the standard set for finite cardinality.
>
Which is SOOOO different from infinite cardinality. Thank God Bigulosity
doesn't suffer from such inconsistency.

--
Smiles,

Tony
.

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