Re: Orlow cardinality question

In article <MPG.1d220cda90688e07989e66@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1d20aa2fd87a730a989e42@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
> > > > TO evades the issue by saying that "TO-size" is not the same as
> > > > cardinality, but without saying what "TO-size" actually is.
> > > >
> > > > Does TO at least agree that for any sets A and B,
> > > > (a) if Card(A) > Card(B) then TO-size(A) > TO-size(B)
> > > > (Bigger cardinality implies bigger TO-size)
> > > > and
> > > > (b) if TO-size(A) = TO-size(B) then Card(A) = Card(B).
> > > > (equal TO-size implies equal cardinality)
> > > >
> > > Yes, that would be fair to say. Bigulosity makes finer distinctions than
> > > cardinality, but doesn't eliminate what distinctions cardinality DOES
> > > make.
> >
> > But so far, while cardiality is capable of comparing any two sets for
> > releative size, bigulousity is not.
> > Which makes Bigulousities, at best, partially ordered, whereas
> > cardinalities are totally order, and even well-ordered.
> >
> Actually they seem minimally and pretty poorly ordered, if you ask me.

When "Bigulosity" measurings can be said to be well-ordered, or even
totally-ordered, only then will TO have any basis on which to criticize
measures of cardinality. Until then, no one will ask him.
.

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