On Jan 6, 7:18 pm, Virgil <vir...@ligriv.com> wrote: > In article > <c0440244-4535-4b3f-8e2d-52e086b7c...@lb9g2000pbb.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > For each value of d, the range is a finite subset of d+1 values in [0,1]. > > > You may properly may say that the codomain for each d is [0,1], but the > > > range is the set of values values actual taken by the function, and for > > > each value of d the range is a set of d+1 values, not an interval. > > > > Wrong again, Ross! > > > -- > > > Ah, that's (partly) fair > > That's totally fair. > > Garbage snipped. > --
Meh. (General spiel at Virgil's expense omitted, though I readily produce them.)
Apocryphally: "But what is much more widespread than the actual stupidity is the playing stupid, turning off your ear, not listening, not seeing."
"Joy in looking and comprehending is nature's most beautiful gift."
"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability."
Well readers I thank you for this chance to soapbox these notions of novel treatments of the reals. And yes, I am interested in any mathematical fault of mine. And, I'm more interested in developments in foundations for novel applications, and sublime facts about our numbers.
So, we know from Goedel's theorems of incompleteness that there are already true things about these objects of our domain of discourse, not theorems of the regular axiomatization, that would be mathematical fact, and as so would direct our course in physics. ZF's universe in a naive set theory contains itself, as does the Universe, as mathematical, or set. The closer we find atoms in reality the smaller they are found, the farther we look the more there is. The infinitesimal, and infinite, does have a place not just in our lofty esteem but as the abstract of our concrete. And, there yet remains to be found what that is, in mathematics.
Then for the infinitely many real numbers from the origin, for the beginning, that's: The End.