On Dec 2, 1:33 pm, Virgil <vir...@ligriv.com> wrote: > In article > <c5d33f48-7659-4a59-a1e4-ac7d100f0...@vy11g2000pbb.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > Valid EF is just the one function, standardly modeled by those finite > > initial approximations with the integers bounded above. > > Except that there is no "Valid EF", given Ross' definition of how it is > to be obtained. > > > > > Funny, I respond to points with points and you remove them from your > > replies > > Once garbage is identified as such, it should be put away as quickly and > firmly as possible. > > --
EF is as simply described as other functions with analytical value like Dirac's delta and Heaviside's step. Funny there's ready interest when I describe it in person, including with the description of the caveats and the importance of mathematical rigor and its satisfaction thereof, outlining the development, context, significance, reservations, questions, and avenues for research.
(And Gorin and Kukushkin go about integrating the staircase with division by zero, I don't expect you to proffer much of an opinion on that.)
So, why don't you go lamenting that Dirac and Heaviside's useful results are taught daily in the curriculum of the reals. In fact I encourage you to make that your personal cause, though, there's been a lot of development since the 70's so there'd be some reading involved to catch up to today's.
While you're at it, go about re-Vitali-izing measure theory, go about noting Banach and Tarski's interesting results in doubling the line, note that the universal set is Russellized already with the compactifying sputnik of quantification, note that the real physical universe as a set is all of its subsets (and Kolker's opinion on that is "no opinion"), and explain why and how configuration of physics experiments computes ratios of "dark" matter, ah, never mind, you've claimed yourself willfully ignorant of anything extra your limited standard.
While you're at it, bring forth any application solely due transfinite cardinals, it would make you famous. Ah, never mind, none are known in the standard and you're not much for independent results (though I do describe a use for transfinite cardinals in probability, and there are transfinite cardinals yet simply not so fundamental to the real, of course as concrete).
Amigos y amigas, or casually friends as I'd so address you, friends: yes, Goedel does prove that there are true facts, about the objects of our theory, not theorems of our standard theory: there are true theories, extra our standard theory. Those real truths are of profound interest to the philosopher.
And then, yes, conscientious mathematicians interested in fundamental truths of mathematics, and mathematicians in the applied as most of us in our white-collar endeavors, or at least for engineers for example a windowpane check or as you would, would be sincerely expressive of interest in new mathematical truths they didn't have to defend from the backward and willfully ignorant, and they're interested.
So I'll have it that yes, Virgil, even you could learn these new things.