Re: infinity

In article <MPG.1da499fa6473c61f98a3a5@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:

> Matt Gutting said:

> > I think the point is that by referring to "the largest multiple of
> > 17" you are assuming that such a multiple exists, i.e. that there
> > exists a multiple of 17 such that no multiple of 17 is larger. Do
> > you in fact contend that this statement is true? If so, how might
> > one represent the number which needs to be multiplied by 17 to
> > produce that "largest multiple of 17"?
> >

> >
>
> No of course there is no largest in that set. The point is that,
> whether we can identify any such largest element in the set or not

No! The point is whether any such "largest" even exists, or not. IT does
not, and no slight-of-hand by TO will make that nonexistence go away.


,
> if Phi(x) is true for all x in the set, then we can assume that for
> any candidate largest we might consider, Phi(x) also holds. There
> will always be a larger x than any we consider, but Phi(x+1) will
> hold as well.

> if all elements are finite, then all differences are
> finite, and any maximum difference we might consider as the range of
> the set is finite.

This stupid mantra that an unbounded set of numbers can have a finite
"range" is just as stupid as the first time TO produced it.

Unbounded sets do not have any "range" at all , at least as TO define
the "range" of a set.


> There is no possible infinite difference in the
> set. This is the way value range has been defined.

If there is no maximum difference of values in a set, the "range" of
that set is not defined, at least by TO's definition. Such a set does
have an infinite diameter, though.
.