In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 16 Mrz., 16:13, fom <fomJ...@nyms.net> wrote: > > > Where we come to the question of > > how you refer to points without > > an implicit use of infinity. > > All points that you can define geometrically, belong to a finite > collection.
Do you mean that every point of a line segment, which points are each defined by the two endpoints of that line segment and real between 0 an 1, belong to a finite collection? > > > > This, of course, comes back to > > how you refer singularly without > > an implicit use of infinity. > > A unit can be defined without referring to infinity. I think it is one > of the silliest arguments of matheology that infinity is required to > define finity. It is simply insane.
WM may well be the one insane but the standard mathematics he labels as matheology is not.
If there were nothing other than WM's "finity" why would we ever need a definition for it? The purpose of any definition is to distinguish between the definiendum and everything else, and has no purpose unless there is something else that can be distinguished from it.
So in order to even think of "finity" one must have something else to contrast it against. Thus sowing that WM has little understanding and less wit.
The same bsic definition distinguishes between them: A set is FINITE if no injection to any proper subset exists and is INFINITE if at least one such injection to a proper subset exists.
WM has frequently claimed that a mapping from the set of all infinite binary sequences to the set of paths of a CIBT is a linear mapping. In order to show that such a mapping is a linear mapping, WM must first show that the set of all binary sequences is a vector space and that the set of paths of a CIBT is also a vector space, which he has not done and apparently cannot do, and then show that his mapping satisfies the linearity requirement that f(ax + by) = af(x) + bf(y), where a and b are arbitrary members of a field of scalars and x and y are f(x) and f(y) are vectors in suitable linear spaces.
By the way, WM, what are a, b, ax, by and ax+by when x and y are binary sequences?
Until these and a few other issues are settled, WM will still have failed to justify his claim of a LINEAR mapping from the set (but not yet proved to be vector space) of binary sequences to the set (but not yet proved to be vector space) of paths ln a CIBT.
Just another of WM's many wild claims of what goes on in his WMytheology that he cannot back up.
NOTE: there is a way to to make the mapping in questiona linear, but it is so mathematical that it is almost certainly well beyond WM's abilities. --