In article <67c38928-9314-44de-bce5-e884f1fe8cb4@l28g2000vba.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 9 Jun., 20:58, Virgil <virg...@nowhere.com> wrote: > > In article > > <13ee1342-16b3-47ed-8cb4-48900dab1...@o36g2000vbi.googlegroups.com>, > > > > > > > > > > > > MoeBlee <jazzm...@hotmail.com> wrote: > > > On Jun 9, 10:36 am, MoeBlee <jazzm...@hotmail.com> wrote: > > > > > > Or do you mean: > > > > > > S is potentially infinite <-> there exists an ordering R on X such > > > > that there is no R-maximal member of X > > > > > Correction (and incorporating Virgil's remark about the empty set): > > > > > S is potentially infinite <-> (S is non-empty & there exists a linear > > > ordering R on S such that there is no R-maximal member of S). > > > > > But, isn't that equivalent with 'infinite' (i.e. 'not finite', i.e., > > > not equinumerous with any natural number') anyway? > > > > It is! So if that is WM's definition, it is the same as at least one > > definition of actual infiniteness. > > My definition is: The union of finite segments is a finite segment. > There is always a last segment. But it can be surpassed.
That does not appear to be a definition of anything, but might possibly be an axiom. > > The idea that the infinite union of finite segments1 > 1,2 > 1,2,3 > ... > results in an infinite segment is false.
The idea that an INFINITE union of finite "segments", no two of which are identical, must result in a finite segment is not even false. It is ridiculous. > > You can verify this by forming an infinite union of finite segments > 1 > 1 > 1 > ... > > If the infinite union of finite segments always yields an infinte > segment
Wm seems to think the the union of {1} and {1} must be a set containing more than one element.
In unions, no greater-than-one number of repetitions of any one element counts more than a single instance of that element counts.
In a unions, one only considers distinct objects, so WM's alleged union is of only one object.
> why then is the result of this infinite union not an infinite > segment?
Because that is not how unions work, at least in any sensible form of mathematics. What goes on in WM's peculiar non-mathematical world is only his own problem, not ours. > > Briefly: The set of all natural numbers that exists has always a last > element, but potentially infinite sets are not static. They can grow > (and they can shrink).
Not in mathematics.
At least not until WM, or someone, comes up with an axiom system in which those properties WM p[osttulates are less self-contradictory than they are at present.
