On Feb 2, 5:00 am, JT <jonas.thornv...@gmail.com> wrote: > On 2 Feb, 05:21, "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > > > > > > > Decided to start a program. An outline of my program follows. > > > Regards, > > > Ross Finlayson > > > A Program to establish the continuity of points in a line > > > The continuum of numbers is a primary feature of mathematics. Logic > > establishes structures modeling the numbers as abstract things. Most > > simple concepts of symmetry and conservation establish numerical > > constructs and identities. Points in a line are built from first and > > philosophic principles of a logic, and a geometry of points and > > space. Their continuity is established. Fundamental results of real > > analysis are established on this line as of the continuum of real > > numbers. Identities are established for certain fundamental > > properties of real numbers in a line in the geometry. > > > An axiomless system of natural deduction > > Conservation and symmetry in primary objects > > Categoricity of a general theory > > Geometry > > Number theory, analysis, and probability > > Sets, partitions, types, and categories > > A natural continuum from first principles > > The continuum in abstract > > A continuum of integers > > The establishment of a space of points from a continuum > > Drawing of a line in the space of points > > The polydimensional in space > > Features of N > > The infinite in the natural continuum > > EF as CDF, the natural integers uniformly > > Features of R > > Points as polydimensional > > Results in the polydimensional > > Continuity in the real numbers > > Reductio of points in space > > Topological counterparts of the open and closed > > Fundamental results of real analysis > > The complete ordered field in the space of points > > Fundamental theorems of integral calculus > > Apologetics > > Infinitesimals and infinities > > Rational numbers and exhaustion > > The continuum as countable > > Reflection on the drawing of the line as countable > > Cantor's argument and counterexamples > > A constructive interpretation of uncountable > > A retrofit of measure theory > > Applications > > Applications in geometry > > Applications in probability > > Applications in physics > > Oh another copy cat, maybe you did not pass anal exams.
"Posting links to youtube" might be a high art in the short-message world, and I'll agree that the "All your base belong to us" montage is an interesting popular culture motif, vis-a-vis, relevance.
JT, I wouldn't want to mislead you that what I've put forth here is generally accepted. Au contraire I was surprised to find that it's rather revolutionary. That said you'll find I am most definitely for the conscientious investigation and discovery of mathematics in the foundations, and particularly for the applied.
Then, the basic notion of a general theory, of things, then as to geometry, number theory, and set theory, this program has as a goal a foundation for application, analysis in the discrete and continuous, toward mathematics for physics that help explain observed effects extra the Standard Model of physics, and there are those.
It might be remiss to not note that of course there are a wide variety of mathematical developments over time and in history that don't necessarily have as much approbation as they should in the contemporary, with Cauchy/Dedekind/Weierstrass in analysis then to Cantor, Russell, and Zermelo and Fraenkel in axiomatic foundations as "modern". Newton's, Leibniz', and du Bois-Reymond's infinitesimals are notably absent from the one (though Leibniz' notation survives), and primary notions of Kant, Hegel, Frege, Quine, Popper the other. As well, there are modern attempts to formulate these particular notions of the integers as infinite and reals as complete that aren't the standard, in light of and in extension of the standard, for example of Aczel, Priest, Boucher, Paris and Kirby, and Bishop and Cheng.
Then, while there is certainly a reasonable framework for modern, standard, real analysis as of finite exhaustions, as well there remains the infinite and infinitesimal to be truly integrated into the foundations, of the theories of these geometrical, numerical, and other collected and divided objects, in the abstract.
Then, this program as commenced in deliberations in this poor medium of discussion has a simple enough general outline, that seems would trend to some 80-200 pages, has as a simple enough goal then this:
Drawing the line, mathematically
Then, where I'd certainly find it if interest where this general course was already developed, having found it missing, sees for it a place.