In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 14 Mrz., 11:43, david petry <david_lawrence_pe...@yahoo.com> > > > Notice that that argument doesn't require the use of an actual infinite. > > > This statement is easily falsified.
Actually not, at least by WM who is unable either to verify or falsify much in his WMytheology and even less outside it. > > The diagonal will not be an irrational number unless it has a finite > definition (which it has not in general Cantor-lists) or has aleph_0 > elements.
The Cantor "diagaonal" argument does not require that anything exist, it only says something about what happens if certain things do exist.
It only says: IF a countably infinite list of infinite binary sequences exists THEN there is an infinite binary sequence not in that list.
Note that it does not require that anything infinite, neither binary sequence nor list of binary sequences, actually exist.
And so it is true in WMytheology, just as anywhere else.
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?
If a = 1/3 and x is binary sequence, what is ax ? and if f(x) is a path in a CIBT, what is af(x)?
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. --