Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:

On 10/05/2024 02:57 PM, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

On 05.10.2024 15:57, Alan Mackenzie wrote:

[ .... ]

I first came across the terms "potential infinity" and "actual infinity"
on this newsgroup, not in my degree course a few decades ago.

[ .... ]

If these terms had any significance, they would still be taught in
mathematics degree courses.  Otherwise, bright students would become
aware of them and catch out their teachers in inconsistencies.  Some
such students are almost incredibly bright, and catching out teachers
is something in the nature of a sport.  It happens rarely, but is
satisfying for all concerned when it does happen.

The "actual" and "potential" is rather common usage
and is usually used to explain "bounded" and "unbounded".

Assuming you are a maths graduate (are you?), were these terms used in
your degree course?  "Bounded" and "unbounded" are explainable without
them.

[ .... ]

You never heard of "actual infinity and potential infinity"?

Up until reading them on this newsgroup, as I said, I had never
encountered these terms.

I must most surely assume you rather have, ....

Thanks for taking me at my word.

.... then thinking that your students ....

I've never been a teacher, hence have never had students.

.... don't need it to understand the surrounds, have that it very much
is what it is, the distinction between the possible and the realized.

That distinction may be unimportant.  It could be that the notion of
potential infinity as an ongoing process is what has led many
mathematically less adept people to assert things like 0.999... < 1.

So far, all we've had about "actual" and "potential" infinity is their
definitions.  Fair enough.  What's missing is an example of a situation
where assuming something to be potentially infinite would give a correct
result, but assuming it to be actually infinite would give a wrong
result.  Or vice versa.  Or something like that.  If there are no such
situations, then the distinction between these two sorts of infinite is
not mathematically significant.

[ .... ]

I mean, you do know a difference between potential and actual as it
relates to infinity? You agree that there is such a thing.

You mean, that there is a difference?  I remain unconvinced.

[ .... ]

--
Alan Mackenzie (Nuremberg, Germany).