In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> Please complete this sentence: "That is clear because my proof rests > upon the premise that actual infinity is a meaningful notion."
The sentence, while complete as it stands, represents a lie too often asserted and repeated by WM.
That the truth of the claimed result need be or ever has been at all clear, at least to anyone except WM himself, is a lie by WM.
The claim that WM's alleged proof is based on any properties of actual infiniteness, other than the mythical ones only extant in Wolkenmuekenheim, is a lie too.
> > If actual infinity was existing as a meaningful notion, then we could > remove all finite lines without changin the union in any way.
Perhaps in WM's Wolkenmuekenheim, but not outside it, and everyone, other than WM himself, resides entirely outside Wolkenmuekenheim.
Outside of Wolkenmuekenheim, there are lots of ordered sets which contain a smallest member and for each of their members also contain a strictly larger member. All such sets, at least those outside Wolkenmuekenheim, are actually infinite sets. And none of them , being outside Wolkenmuekenheim, behave at all as WM says they must.
WM's power to make things behave the way he wants them to exists only within the borders of his mythical Wolkenmuekenheim, and nowhere outside of it. --