On 8 Mrz., 22:57, Virgil <vir...@ligriv.com> wrote: > In article > <ed9dbe7d-6b3b-4acc-86bc-7b8408236...@m4g2000vbo.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> 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. > A nice confession of intellectual helplessness. Of course the lines from 1 to n are completely irrelevant. That can everybody with elementary knowledge recognize. > > > Learn: In mathematics, we have sets of natural numbers without last > > elements. > > > 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.
I let this stand as it is although (or because) it has nothing at all to do with the problem that every set of natural numbers, i.e. a set that contains natural numbers, has a first element which fact Virgil objects to.
