Re: Relative Cardinality


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.
>
> 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.

But to represent a particular integer, you only need a _finite_ number
of symbols, which was the point!

--- Christopher Heckman

> > And even unboundedly large does not require infinitely large, as there
> > are no infinitely large rationals or reals, though both are unbounded.
>
> Regards, WM

.

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