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

On 11/2/2024 6:01 PM, Ross Finlayson wrote:

On 11/02/2024 12:37 PM, Jim Burns wrote:

On 11/2/2024 2:02 PM, Ross Finlayson wrote:

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

of often for induction arbitrary m and larger n,
is well-known to all students of calculus.
>
"The infinitesimal analysis", ....

>
The delta.epsilonics well.known to students of calculus
is not infinitesimal analysis.
For δ > 0 and ε > 0
there are _finite_ j and k such that
δ > ⅟j > 0 and ε > ⅟k > 0

The delta-epsilonics is
a perfectly suitable approach to defining
infinite limit in theories of infinitesimal analysis.

The delta.epsilonics well.known to students of calculus
is not infinitesimal analysis.
For δ > 0 and ε > 0
there are _finite_ j and k such that
δ > ⅟j > 0 and ε > ⅟k > 0

How about atomism, is there a theory there with
truly abstractly uncuttable objects like the
theoretical atom?

There are lots and lots of theories.
There is one theory
(modulo lots and lots of ways to express it)
of the rationals with just enough points more that
continuous curves which cross must intersect.
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.