Re: Replacement of Cardinality (effective bounds)

On 08/25/2024 10:47 AM, Jim Burns wrote:

On 8/24/2024 8:26 PM, Ross Finlayson wrote:

On 08/24/2024 03:39 PM, Jim Burns wrote:

On 8/24/2024 4:50 PM, Ross Finlayson wrote:

On 08/24/2024 11:08 AM, FromTheRafters wrote:

WM has brought this to us :

Le 23/08/2024 à 20:06, joes a écrit :

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The unit fractions don’t reach 0.

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Of course not.
Therefore they must cease before.

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Why must they cease at all?

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He can just axiomatize it so,
saying that there's a rule.

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Yes, clearly, WM can do it.
Much less clear is why WM would do it.

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Still, you can just look at it that
he has a speech impediment,
and in some generous reading
he's the only go-between that somehow
you must explain in his terms, what's in your terms.

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You mean, I must explain like this?
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In a finiteⁿᵒᵗᐧᵂᴹ order ⟨A,<⟩
each non.empty subset S ⊆ A holds minᑉ.S and maxᑉ.S
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I will consider doing that.
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So here, it's simplest as
a system of bounds, modeled in the unbounded,
instead of just
a usual system of no bounds, modeled in the unbounded.
I.e. it's just the sort of opposite that you've chosen
or have a natural or imposed sort of slur about
whether they're bounds in the unbounded
or not-bounds in the un-bounded.

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Huh?
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Anyways
you've declared many times that
you're quite deaf to claims that
Russell's axiom is in any way false,

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Since I like to know what I'm declaring,
what is Russell's axiom?
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Speaking of axioms in general,
it is a theorem that,
if the axioms do not imply a contradiction,
then they are not false of _everything_
then a model exists.
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Also, too,
if a model exists,
if the axioms are not false of _everything_
then the axioms do not imply any contradiction.
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so,
I'm not quite sure what it is
that will make it so that
anyone who'd care to try and follow your argument
would have to always insert
a slate of boilerplate argument

>
The usual practice in mathematical argument is
to insert the boilerplate text once, somewhere,
and then pass to the alert reader the job of finding
the relevant previous paragraph or previous chapter
or previous volume or previous school.
>
My (questionable) understanding is that it's considered
insulting to always insert the boilerplate.
Perhaps it's seen as tacitly calling the reader
less.than.alert.
>
>

Russell's retro-thesis is that there's an ordinary
well-founded inductive set, when already it's shown
that Russell's antinomy would affect such a thing,
it's an axiom contradicting what would have been.
So, yes, your rule number one is considered intrusive
as you put it, because, there's already an implicit
where it's not so, that the whole "restriction of comprehension"
bit is contrived, and that's not that "three-sided polygons
are triangles" is anything other than a matter of definition,
it's that "three-sided polygons don't exist" is a restriction
of comprehension, that thusly is either always intrusive or
always capricious.
Either way it's not my pick.