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

On 10/21/2024 09:21 AM, Jim Burns wrote:

On 10/20/2024 8:20 PM, Ross Finlayson wrote:

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.

>

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.

>
Microscopes and
finite sequences of only not.first.false claims
are powerful tools.
>
Do you refuse to use microscopes or
knowledge from microscopes?
>

Anyways you still haven't picked "anti and only".

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I vaguely recall that
you (RF) made some incorrect claims about
Cantor's  argument from anti.diagonals,
and you asked for my participation in some way.
Could you refresh my memory? TIA.
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>

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I'm not much inclined since you ignored it
about ten times because what it is is that
it uses the same reasoning for the anti-diagonal
result that there are no Cartesian bijections
between domains of different cardinalities to
show that the non-Cartesian function with
only one diagonal the only-diagonal exists
and is not so precluded.
>
Yet, I'm inclined because it's always true,
and in the case that you really have these
recurring gaps in your memory, that over the
past several and more months there's been
at least ten mentions of this here on sci.math.
>
We were discussing Zeno and mathematical continuity
and I kept pointing out you were missing out on
the fuller dialectic and indeed that there are
plain inductive arguments to spoil your plain
inductive argument, thus _requiring_ a fuller
deductive argument and explaining how indeed
the "infinite limit" does reach the sum, and
as with regards to the "continuum limit" of
functions, that in the continuum limit the
line integral exists and in the continuum limit
these line-reals exist, then I pointed out that
the very same reasoning of the anti-diagonal
argument itself, which I sort of ignore because
it's not constructivist usually in the sense of
imputing what it doesn't and contradicting itself,
that: there's correspondingly an only-diagonal
argument that line-reals result from a function
that has a discrete range and continuous, and
countable, domain.
>
Then I suggested that I would put anti-diagonal
in one fist, only-diagonal in the other, then
hide them behind my back and perhaps exchange
them, then that you get to pick.
>
You get to pick, was the idea, then I laughed
and said that I had put them together, so,
you get both or none.
>
"You" here meaning anybody, ..., because it's
a mathematical statement so is the same for anyone.
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