In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 12 Mrz., 11:08, William Hughes <wpihug...@gmail.com> wrote: > > On Mar 12, 10:19 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 12 Mrz., 00:51, William Hughes <wpihug...@gmail.com> wrote: > > > > <snip> > > > > > > > > > > There is a fixed column, C_1, which is coFIS to > > > > |N. There is no fixed line which is coFIS to |N > > > > > There is no |N in potential infinity. > > > > |N is the potentially infinite set of natural numbers. > > > The "potentially infinite set" is already a contradictio in adjecto, > because the notion of set always requires completenes.
The notion of set only requires an unambiguous test for membership, at least outside of Wolkenmuekenheim. And |N has one. > > > > There is a problem with the statement, of actual infinity, that all > > > natural numbers are in the list but not in any single line. > > > > Note, in Wolkenmuekenheim > > all natural numbers are in the list but not in any single > > findable line. > > No, there are not *all* natural numbers in any healthy mathematical > theory. Have you read hundreds of posts without learning that basic > stuff?
It is WM who has not learned the basic stuff about sets, that there can be no such thing as a potentially infinite set, because there can be no unambiguous test for whether given object is a member of such a "set". > > > > There is no difference between "actual" and potential > > infinity as long as we restrict things to > > findable quantities. > > If you are incapable of learning what potential infinity means, as it > is suggested by your statements above, then your assertion is > understandable but nevertheless wrong.
It is WM who has not learned the basic stuff about sets, that there can be no such thing as a potentially infinite set, because there can be no unambiguous test for whether given object is a member of such a "set". > > Actual infinity requires that *all* natural numbers are in the list > but not in a single line. That is a contradiction.
Only in WMytheology. When there is a first line as a set and every successor line is the successor set then as soon as there is the set of all lines there is a union of all those line-sets.
In WM's world, it appears to be a requirement to allow a set of sets for which no union of its members is allowed.
> Since they are, in > fact, not in a single line (since there is no last findable line), > only the other alternative
For any set of lines, each of which is, among other things, a set, then in any and every standard set theory, there must be a union of all the lines/sets in that set, whether those lines/sets are "findable" or not.
At least everywhere in standard mathematics, however skewered WMYTHEOLOGY may get.
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. --