On Feb 26, 9:59 am, "Brian M. Scott" <b.sc...@csuohio.edu> wrote: > On Tue, 26 Feb 2013 08:19:02 -0800 (PST), "Ross A. > Finlayson" <ross.finlay...@gmail.com> wrote in > <news:email@example.com> > in rec.arts.sf.written,sci.math: > > > On Feb 25, 3:18 pm, "Brian M. Scott" <b.sc...@csuohio.edu> wrote: > >> On Mon, 25 Feb 2013 14:11:50 -0800 (PST), Quadibloc > >> <jsav...@ecn.ab.ca> wrote in > >> <news:firstname.lastname@example.org> > >> in rec.arts.sf.written,sci.math: > >>> On Feb 25, 3:20 am, "Brian M. Scott" <b.sc...@csuohio.edu> wrote: > >>>> Good grief. Is that crackpot still around? > >>> Who, me? > >> No, Ross Finlayson. > > [...] > > > Get used to it. > > No need: I've not read sci.math in years. Some idiot added > it to this thread, and I didn't notice immediately. > > > Those things are true, what I wrote: nothing more, > > nothing less > > What you wrote was partly false and partly just nonsense. > > [...] > > > Ross Finlayson > > B.S., Mathematics > > You should ask for your money back. Or remove the comma.
But, I got a full ride.
You deserve a Ph.D. if you've contributed in your dissertation a novel advancement of human knowledge and here mathematics. And a practicum isn't a thesis.
Piled higher and deeper.
Then back to layman ruminations on mathematical infinity as largely the community here might find science and speculative fiction of particular insight and perspective, for hard science or the fantastical in compelling themes, no, transfinite cardinals have not yet found a particularly suited place in physics. That's not for lack of trying.
From the unbounded to the infinite in the large, the universe, to the microscopic and atomic and infinitesimal, the universe, physicists today ponder how there are infinitesimal strings some as many orders of magnitude smaller than the hydrogen nucleus as fundamental point particle than it is to us, and how the universe is as many orders of magnitude more grand than all our anthropocentric view can partake around us. They confront these notions that reflect, as far as is logical in expectation, mathematics, the Platonist of what is. And, it is what it is. Where traditionally mathematics led physics, our modern globalized experiments leave us more data than the mathematics, of the day, contain.
The Universe, as set, of its elements, for all functions from things to things, exists.
And, Zeno of Elea's archer's arrow: finds its mark. Satisfactorially, if perhaps only partially resolved in methods of exhaustion since even the simple consideration of potential and actual in the infinite (and not all of Archimedes' infinities are Archimedean): that analysis of the continuum with its perfect results is in the countable.
The Universe exists and would be its own powerset: a contradiction to that it is a regular, well-founded infinity. (And there are quite modern theories with irregular infinities that have little to do with large cardinals, which, in a well-founded universe, would simply be cardinals already.) A paradox, some might say, but the Universe, or via MWI or "multiverse" one and the uni-verse, exists and we are only in it. The collection of all ordinals, would itself be an ordinal. Russell's set of all sets not containing itself, does, exactly as what would be the well-founded universe, would be.
So, measure theory founding real analysis uses countable (and only countable) additivity for all results as they match results of geometry, for evaluating area, and, though shoehorned into measure theory (for simply the the non-measurable instead of the polydimensional of Vitali's points), transfinite cardinals as supposed foundation, for mathematics, find yet no edifice, as physics.