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

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

On 11/04/2024 03:52 AM, Jim Burns wrote:

[ .... ]

The delta-epsilonics of course,
or some put it "delta-epsilontics",
with little d and smaller e,

That one theory is
the theory well.known to students of calculus.

I mention this
(and mention it and mention it)
because
I am declining your invitation to
be the mark in a bait.and.switch.

Sure it is, the delta-epsilonics is well known,
and where often proofs in geometry will have been
introduced vis-a-vis usual sorts of plain "checks"
as "proofs", then delta-epsilonics is often the
first sort of deductive account, introduced to
what's usually upper-class secondary students,
then that the concept of the infinite limit
is made and then it's pointed out how that fits
with regards to classical expositions like Zeno's,
of what yet doesn't.

What I'm saying is that since antiquity,
it is known,
that there are at least two models of continuity,
and you may call it Archimedean and Democritan,
about the field of rationals versus atomism,
and that infinitesimal analysis includes both.

So, no, I'm not interested nor was it proffered
"bait-and-switch", though here there's still
the "pick one, get both".

The "clock arithmetic" is usually fmailiar to
students as with regards to the sweep of
the secondae hand around the clock, or as
with regards to the rollover of the odometer,
that a course-of-passage in _time_ is most
simply as in accords with the classical expositions
of constant and uniform motion.

Indeed the dialectic I should hope you know as
something akin to "thesis, anti-thesis, synthesis",
as with regards to that being "pick one, get both".

I.e., the complementary duals, these competing concerns,
meet in the middle, even if: "the middle of nowhere".

So, infinitesimal analysis includes delta-epsilonics,
if not the other way around.

Then, some "continuum infinitesimal analysis",
makes for "Standard Infinitesimals" like
these "iota-values" of "line-reals".

constant monotone strictly increasing

extent density completeness measure

Ross, that post, like so many of yours, displays only local coherence.
Each sentence looks like it would make sense if only one were to read the
surrounding context.  On doing so, no overall sense is to be found, just
a vague drift from allusions to topics, never quite settling on anything
definite.

In this, your posts are a bit like Edith Sitwell's poems in Façade:

'Do not take a bath in Jordan, Gordon,
On the holy sabbath, on the peaceful day!'
Said the huntsman, playing on his old bagpipe,
Boring to death the pheasant and the snipe -
Boring the ptarmigan and grouse for fun -
Boring them worse than a nine-bore gun.
Till the flaxen leaves where the prunes are ripe,
Heard the tartan wind adroning through the pipe,
And they heard McPherson say:
'Where do the waves go? What hotels
Hide their bustles and their gay ombrelles?
And would there be room for me?'

--
Alan Mackenzie (Nuremberg, Germany).