In article <eb95bd31-1206-411a-a936-f93a8ec5205e@g37g2000yqn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 31 Mai, 03:12, "Peter Webb" > > > Show me a complete finite linear set that does not allow for > > quantifier reversal. > > En Am: m =< n <==> Am En m =< n [*] . > > > > ************************ > > Its your proof. Either provide such a set yourself, or prove that none > > exists. > > [*] belongs to the basic logic of finite sets. As this logic has been > obtained by observing the behaviour of finite linear sets, there is no > further proof except that a finite linear set violating [*] has never > been observed.
It still requires that which WM is incapable of providing, namely a proof. > > > > Therefore: Either [*] holds or the set is not complete but allows for > > extension.
It still requires that which WM is incapable of providing, namely a proof.
> > > > ***************************** > > You better define "extension", and show its relationship to "complete". Just > > in case, you better define "complete" as well, in case you are using it > > differently to everybody else. > > Complete means that every element of a set exists.
Then N is complete.
> In case of a linear > set, complete means that also the last element of the linear order > does exist.
If that is a part of WM's definition, then WM need to prove that no "incomplete" set can exist, something that he has been failing to do for years, at least without assumes it a priori.
. > > Then we have only > > En Am: m =< n ==> Am En m =< n [**] > > because not all elements are readily available. > > > > ************************** > > You better define "readily available" while you are at it. > > Every element of a complete set is readily available.
That does not define anything.
> If not eery element is readily available, then the set is incomplete, > that mean not complete. > > > > That is called a potentially infinite set.
Except that there are no such things.
> > > > ************************* > > Define "potentially infinite" as opposed to "infinite". Show that this does > > not allow uncountability to be proved. > > Potentially infinite is not opposed to infinite but is one kind of > infinity. The other one is actually infinite. > > > > > Resume: The internal contradiction in set theory is veiled by mixing > > up potential and actual infinity. That is the reason why set theorists > > usually refuse to specify which infinity they apply. Most even pretend > > (or profess) not to know the difference.
Sure they do. One major difference is that otentially infinite sets do not ever exist but actually infinite sets exist in many set theories. > > > > ************************* > > What *is* the difference? > > > Potential infinity is possible, actual infinity is not.
Backwards as usual. > > > > ************************** > > Gee, such a big claim you make. Yet no proof. Not even a lame attempt. > > Sorry, you are only unable to understand it. Not everybody is able to > understand everthing. That is an odl wisdom. > > > Even > > cranks generally try and produce bad proofs, > > Yes, set theorists, for instance. But I have shown that they need to > use logic of potential infinity to "prove" their actual infinity.
Wm keeps claiming to have "shown" all sorts of things, but until the recipients of his "showings" acknowledge the validity of such "showings", WM has shown nothing but his ignorance to anyone.
It was not Wiles "showing" a proof of FLT so much as the rest of the world's acknowledging its validity that was important, since he was nowhere near the first to claim a proof of FLT.
When WM can successfully square a circle, trisect an angle and duplicate a cube using only the classical methods, only then will anyone here be liable to accept WM's proofs that all sets are necessarily finite in any and every set theory.
