Re: infinity


Tony Orlow wrote:
> Randy Poe said:
> > That was the mantra (one variant): that if no two elements are
> > infinitely far apart, the range is finite.
> That is exactly what I mean by a range of values: a maximum possible difference
> between values.

And if there is no maximum possible difference?

> If no two values have an infinite difference between them, if
> it is not possible to have an infinite difference between values, how can the
> set be said to have an infinite range of values?

Because there is no finite range that serves as an upper limit
on the possible finite differences.

There is no maximum to the finite differences.

If you want to talk about an upper bound to the finite differences,
it isn't a finite value. Therefore we can reasonably say "the
range is infinite" since it isn't finite.

> The set of finite values is unbounded and there is no finite value greater than
> all of them,

There you go.

> and yet they are all finite by definition.

Right.

> So, while what you say
> may be true for any given finite value, it is not true for the set of all
> finite values.

What isn't? You just gave the relevant property of the set. Note
that your sentence above begins "The set of finite values". Are you
saying that what follows, even though it is a property of the
set of finite values (no upper bound), is not true for the set
of finite values (no upper bound)?

- Randy

.

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