On Nov 30, 8:16 am, FredJeffries <fredjeffr...@gmail.com> wrote: > On Nov 26, 9:19 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com> > wrote: > > > > > > > > > > > On Nov 26, 12:03 pm, Virgil <vir...@ligriv.com> wrote: > > > > In article > > > <ba2d403e-154a-46d2-9fc9-6e5ae92ed...@vy11g2000pbb.googlegroups.com>, > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > On Nov 25, 11:22 pm, Virgil <vir...@ligriv.com> wrote: > > > > > In article > > > > > <be566287-1de6-426b-a9d8-420bb9279...@n2g2000pbp.googlegroups.com>, > > > > > "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote: > > > > > > > EF is simple and it's defined simply as a function, not-a-real- > > > > > > function, standardly modeled by real functions. Dirac's delta and > > > > > > Heaviside's are as so defined, as functions, not-real-functions, > > > > > > standardly modeled by real functions. And, the definition of function > > > > > > itself, here is modern and reflects over time the development of the > > > > > > definition of what is a mathematical function. Then, in actually > > > > > > extending the definition of what are the real numbers, in A theory, it > > > > > > is directly defined, and applied. > > > > > > > There are hundreds of essays on it here. > > > > > > Then give a reference to some of them, preferably by someone other than > > > > > yourself. > > > > > > In particular we need a mathematically satisfactorily definition of your > > > > > alleged EF, again preferably by someone other than yourself, which will > > > > > take it out of the realm of mythology. > > > > > -- > > > > > I wrote all that. > > > > Did you? > > > > I certainly do not ever recall seeing your alleged EF adequately > > > presented, and see now no references to where one might see it > > > presented, whether adequately or not. > > > > And if you still will not provide a reference to it, a url, or something > > > through which anyone can access it to see it for him or her self, it is > > > as if no such thing ever existed. > > > > Which in the absence of any evidence to the contrary, I will continue to > > > assume. > > > -- > > >http://mathforum.org/kb/search!execute.jspa?forumID=13&objID=f13&forc... > > at least hundreds of results > > >http://mathforum.org/kb/message.jspa?messageID=7888348"Cantor- > > Finlayson theory" > > >http://groups.google.com/group/sci.math/msg/af29323d694cf89e1999- > > "Equivalency Function" > > >http://groups.google.com/group/sci.math/msg/ccb0941dc3421afdperhaps > > the first mention > > > Do you know the old saw about "assume"? > > > My friends, or as I would so address you, the definition of EF is > > written in some few lines: constantly monotonically increasing from > > zero through one. > > You've had this function for 13 years now and you STILL can't > calculate the area of a triangle with it.
Fred Jeffries who I respect: I'd like to think that's in the context of modeling Dirac's delta with triangles or radial basis functions, but what's important to describe of EF as plotted is this: removing all the space between the integers and plotting the elements in the range it would look like f(x) = x from zero to one, half a square and a triangle, but the F-Sigma Lebesgue integral of EF evaluates to one not one half, now that's the surprise.
EF: CDF: of the uniform distribution of the natural integers.