Re: Relative Cardinality

In article <1121246468.314972.117240@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Virgil wrote:
>
> > > By the way, your definition of infinity would also make the values of
> > > natural numbers infinite, because they are not bounded by any fixed
> > > number n_0.
> >
> > WRONG! WM conflates infinitely many with infinitely large. There are
> > infinitely many rationals in any non-degenerate real interval, but in
> > bounded intervals, none of them are infinitely large, so that nfinitely
> > many does not imply infinitely large.
>
> I spoke of natural numbers.

Every natural "IS" a rational, in an obvious sense so that unless WM
insistsa on having infinitely large rationals (and reals and complexes
and quaternions, etc.) he is being clearly inconsistent.
>
> If you represent the natural numbets in the unal system, i.e., 3 = III
> etc, then there are as many strokes as there are numbers. Neither gets
> infinite without the other.

It depends on what one means by infinite in this context. My meaning is
"without end".

The sequence of naturals is without end. But there is no single natural
that is without end.
> >
> > And even unboundedly large does not require infinitely large, as there
> > are no infinitely large rationals or reals, though both are unbounded.
.

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