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

On 10/20/2024 11:33 AM, Jim Burns wrote:

On 10/20/2024 12:30 PM, Ross Finlayson wrote:

On 10/20/2024 06:36 AM, Jim Burns wrote:

>

Is there some sort of protocol
which you (RF) recognize
in order to talk about a thing
and not.talk about things not.that?

>
Here there's freedom of speech it one of
what we call constitutional liberties,

>
I take your answer to mean
"no, there is no such protocol".
>
Surely,
with your degree in mathematics,
you understand that
you are depriving yourself of
the use of a powerful tool.
>
To describe an indefinite one of
an infinite domain is
an infinite force.multiplier.
>
But it needs to be
only those in that domain,
of that description.
>
Loosen the restriction on the discussion,
lose the force.multiplier.
There isn't much useful to be said
about things which _might or might not_
be well.ordered. Etc.
>
>

Au contraire, to the contrary, I proffer
that extending the relevant domain while
keeping it a completely connected relevant
domain _is_ a most proper and surmounting
improvement of the discourse, to include
the wider considerations of a topic in
the _foundations_ of the theory, not
merely a single theorem under a microscope.
This is foundations - the subject matter
and topic is a complete theory of _all_
the mathematical objects, not merely
pet theories.
You describe a vice-grip,
this is both flange _and_ jig.
That is to say, when every tool's a hammer,
yet every site is both flange _and_ jig.
And not merely a nail, ....
Then, where it does involve a bit the more
mental or reasoning resources than the
quaint shadow-box diorama of the pet theorem,
more to it: that's foundations.
A tower of rain, ....
It's like the end of the matrix movies
when Neo and Smith are duking it out in
the rain, the tower of rain, then that one
point where the "force multiplier" of course
makes it so that Smith definitely has a numerical
advantage - I forget how it ends except basically
it just ends.
The "Tower of Rain" that is to say is a
metaphorical concept somewhere very far
above the least initial ordinal in the
cumulative hierarchy - so far above there's
no far below and so that so far above there's
no far above - a tower of rain.
I have great facility with plain linear induction,
for example noticing that for the case with
"this attains to the limit" that there's a
contradictory case "and it's not attained",
explaining why indeed a course of deductive inference
is necessary to understand and correctly explain an
actual resolution and establishment of the infinite
limit, when otherwise is merely empirical and in
the usual sense nominalist and not realist and
fictionalist and not realist and fallibilist and
not realist - though it's a pet theory that you
can pick up or put down very readily.
The idea of greater foundations is that it's a
greater sort of best pet theory, that's the
only one to pick up or put down, with what
otherwise is merely reverie.
Anyways you still haven't picked "anti and only".