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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Wed, 8 May 2024 13:20:25 -0700
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On 05/08/2024 11:40 AM, Jim Burns wrote:
> On 5/7/2024 4:22 PM, Ross Finlayson wrote:
>> On 05/06/2024 12:36 PM, Ross Finlayson wrote:
>>> On 05/05/2024 03:02 PM, Jim Burns wrote:
>
>>>> I think that your wished.for supplements of
>>>> standard.issue quantifiers
>>>> can be defined given
>>>> standard.issue quantifiers.
>>>>
>>>> For my wish,
>>>> I would like everyone to be clear on what
>>>> standard.issue quantifiers and variables
>>>> mean.
>>>>
>>>> I think that,
>>>> way off in that glorious future,
>>>> both you and I will be able to be
>>>> satisfactorily understood.
>>>>
>>>> And what more could there be
>>>> to wish for?
>>>
>>> Well, one might aver that extra-ordinary
>>> universal quantifiers are merely syntactic sugar,
>>> yet there's that in the low- and high- orders,
>>> or the first and final, that what they would
>>> reflect of the _effects_ of quantification,
>>> something like
>>>
>>> for-any A?
>>> for-each A+
>>> for-every A*
>>> for-all A$
>
> My guess is that 'A' is the ASCIIfication of '∀'
> Thus
> for-any ∀?
> for-each ∀+
> for-every ∀*
> for-all ∀$
>
> Please use each of ∀? ∀+ ∀* ∀$ in a sentence.
>
>
> I am familiar with wildcard characters in
> their programming.language context. In that context,
> they look to me more like variables ranging over
> standard.issue.all[1] of a set of characters or
> a set of sequences of characters.
>
> Maybe if you used ∀? ∀+ ∀* ∀$
> I would see better what you mean.
>
>
> [1]
> | ∀x:B(x) ⇒ B(t)
> | ∀x:(B⇒C(x)) ⇒ (B⇒∀x:C(x))
> | B(x)  ⊢  ∀x:B(x)
> | ∃x:B(x) ⇔ ¬∀x:¬B(x)
>
>>> that it is so that the sputniks or extras
>>> of the quantification in the extra-ordinary,
>>> have that a quantifier disambiguation:
>>> is in the syntax.
>>>
>>> Then for the rest of it, like our discussions
>>> on continuous domains and continuous topologies,
>>> i.e. the topology that's initial and final itself,
>>> then these line-reals field-reals signal-reals,
>>> about the integer continuum linear continuum
>>> long-line continuum, ubiquitous ordinals and
>>> extra-ordinary theory, is that these are objects
>>> of the universe of mathematics in the
>>> Hilbert's Infinite Living Museum, of Mathematics.
>>>
>>> When considering someone like Paul do Bois-Reymond,
>>> who came up with the diagonal argument and the long-line,
>>> and Mirimanoff, who came up with the axiom of regularity
>>> and also the extra-ordinary, and for example Peano,
>>> with his integers and infinitesimals, then one may well
>>> aver that today's standard is a tenuous sort of course,
>>> that is much more fully enriched by the first sort of
>>> nonstandard function like the Dirac Delta, then into
>>> the greater realm of the superclassical law(s) of large
>>> numbers, and more replete three definitions of
>>> continuous domains, and the Cantor space(s).
>>
>> That's what I'm talking about.
>
> I think that you are over.estimating
> how clear you've been.
>
> I don't see how standard.issue.quantifiers are
> enriched by the examples you give.
> Standard.issue quantifiers are already rich enough
> to describe them, so, huh?
>
>
> I have had a bit of fun here in sci.math
> brewing up non.standard notation for
> non.standard quantifiers, among other things.
>
> My non.standard notations are abbreviations for
> expressions with perfectly standard quantification.
> For example,
> the ordinals are well.ordered.
> If exists any γ: B(γ)
> then, exists first β: B(β)
> ∃γ:B(γ) ⇒ ∃₁β:B(β)
>
> That's an abbreviation.
> ∃₁β:B(β)  ⇔
> ∃β:(B(β) ∧ ¬∃α<β:B(α))
>
> I am fond of abbreviating.
> But all the interesting stuff is found
> as a consequence of the disabbreviated forms.
> I once spent an entire course studying
> ∫ᵟᶿω = ∫ᶿdω
>
> the generalized Stokes theorem
> https://en.wikipedia.org/wiki/Generalized_Stokes_theorem
>
> It was a very full course.
> A lot is crammed into ∫ᵟᶿω = ∫ᶿdω
>
> Are ∀? ∀+ ∀* ∀$ abbreviations of
> standard.issue.quantified expressions?
>
>

https://en.wikipedia.org/wiki/Fran%C3%A7ois_Vi%C3%A8te