In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 14 Jan., 23:21, Virgil <vir...@ligriv.com> wrote: > > > > yes, but never from all - since all possibilities are in the list - > > > like in the Binary Tree. > > > > So that in the wild weird world of WMytheology, though not elsewhere, > > one can have a thing which differing from each member of a list without > > differing from all members of that list. > > Obviously. The reason is simple: There is no "all" for infinite sets.
If there is no "all" for infinite sets, then one cannot ever say "for all natural numbers" or "for all ratonal numbers' or "for all real numbers" or "for all" of any but members of some specific finitie set. > > > > Yes, it does and it does not. That's called a contradiction. > > > > But note that that only happens in WMytheology. > > > > Outside WMytheology, an infinite sequence differs from each of any set > > of finite sequences, if only by being infinite instead of finite. > > That does not help. It can only differ at finite places.
It takes infinitely many finite "places" to make an infinite sequence. And it is quite legitimate to speak of some property as belonging to "ALL" of those "places" outside of WMytheology, even though the set of such "places" must be an infinite set.
> But since all > finite places belong to finite initial segments, and since all finite > initial segments are in the list, the anti-diagonal cannot differ from > all entries of the list. I know, it is hard for you to accept that, > but infinity does not help.
It should be hard to accept anything so obviously false. at least false outside WMytheology.
An infinite sequence can be different from a different member of your sequence of finite initial segments at each of its infinitely many places, thus differ somewhere from every one of them.
To deny this is to deny the existence of infinite sequences entirely.
Which in turn denies such parts of mathematics as calculus. > > > But according to WM, within his wild wild world of WMytheology an > > infinite sequence can be identical to a finite sequence. > > No, but the infinite sequence consists exclusively of finite initial > segments. > Didn't you know that? It is so.
Infinitely many of them. But it is irrelevant in that it does not justify the idiocies of WMytheology that WM is futilely attempting to foist on the world of mathematics. > > Regards, WM --