In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> > WM confuses "natural number" with "representation > > of natural number" and his intentions to make > > such representations. > > > > That is nonsense. If the natural number is different from the set of > its representations, then one can never have, know, or use it.
WM conflates names with the things named. A numeral, for example is only the name of a number and not the number named.
> Then > one has always to talk about representations of natural numbers.
Using a name normally refers to the thing named as distinct from the name itself.
To refer to the name rather than the thing named, one can use quotes around the name or various other methods, but absent any such evidence of pointing to the name rather than the named, use of a name does not point to that name.
That one cannot put the person named Napolean Buonaparte on this page does not mean that one cannot refer to him by name on this page.
> But > that is silly. Therefore I have written the natural number one here > and here 1.
You have only given two names for the same number.
> If you are of different opinion, that need not be wrong > but irrelevant for the present discussion concerning a list all lines > of whcih can be removed without removing the union of these lines.
So that in Wolkenmuekenheim WM claims to be able to remove every set of a union of sets and still have the same union.
Typical. But invalid outside Wolkenmuekenheim.
> It > somewhat resembles the Binary Tree all finite paths of which can be > removed without removing the Binary Tree itself.
Such trees, binary or otherwise, do not exist outside of Wolkenmuekenheim. Elsewhere removing any path from a tree changes the tree, usually into something that is no longer a tree at all. > > The reason for all this nonsense is the assumption that the union of > finite elements could become actually infinite
The union of infinitely many lines can be an infinite set, at least in any set theory not constrained by having to satisfy the idiotics of Wolkenmuekenheim.
WM has claimed to be able to bijectively map the set of infinite binary sequences , B to the set of reals |R and then that image in |R to the set of paths, P, of a of a Complete Infinite Binary Tree.
Which is perfectly possible for some non-linear types of mappings.
But WM also claims that he can do it with bijective linear mappings, which, for several reasons that WM is incapable of acknowledging publicly, neither he nor anyone else can do. --