In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 8 Mrz., 10:41, Virgil <vir...@ligriv.com> wrote: > > > > A set of natural numbers, finite or infinite, without a first element > > > is not object of mathematics. > > > > > > > Name the first line. > > > > > > Which first line? There are infinitely many possible first lines. > > > > In fact EVERY line is a first line of some such set. > > > > > Name at least one line that is not obviously irrelevant for the task. > > > > Since any line can be the first line of a suitable set of lines, each > > line is relevant, but also unnecessary. > > Each line is relevant but also irrelevant. A nice confession.
In order to determine whether a particular line is in a set of lines covering |N, no line is irrelevant but neither are all all are necessary. > > Learn: In mathematics, we have sets of natural numbers without last > elements.
That is something that WM has yet to learn: that for each natural number in THE set of all naturals, there is a successor natural following it which is also in THE set of all natural numbers. and no proper subset of that set is THE set of natural numbers. Not even in Wolkenmuekenheim.
> A set of natural numbers without a first element is not > object of mathematics.
The empty set is an object of mathematics even if to an object in WMytheology.
And where is WM's proof that some mapping from the set of all binary sequences to the set of all paths of a CIBT is a linear mapping? WM several times claimed it but cannot seem to prove it. --