GFR Wrote:I just doubted that we can put s=0 in a[s]<0>, without warning that perhaps (exceptionally), and in this particular case, a[0]<0> is not the identity operator.
However I never saw a case where \( f^0(x)\neq x \). What is a[s]<0> then in your opinion?
Quote:Well, you are the Organizer of this Forum and its Moderator and you are right in trying to moderate me.
...
Now, please, you may keep aside all unappropriate weapons.
...
Hey, hey, I never moderated you in any way, nor did I mention the possibility. You could and can write freely without restriction what you want on this forum (of course obeying the basic netiquette rules).
I merely want to convey that establishing mathematical theories is not like convincing your sponsor to give money. Certain rules that work well in social communication - for example the more often and by the more people a certain statement is repeated, the more true it becomes - dont work in mathematics. And also building lobbies and parties to support or enforce the own opinions does not work. Quoting authorities does not work either.
Basically it is about providing/proving theorems about definitions which you are free to design yourself. Assessing the beauty and propagating is then again subject to opinions and social communication.
But the start has to be true theorems/derivations.
So the easiest way for you would be just to exclude the case \( r=0 \) in your GML, however whether this increases the beauty is another question. But then zeration is still not determined by the GML (as I showed in the zeration thread, and there are still no uniquness conditions for *your* zeration provided). So what Andrew said in a side sentence:
Quote:I think so far we have established that the GML-hyper-0 is "zeration" as you define it
is not true, as there is no the zeration following from the GML nor is there the zeration following from GML plus additional conditions. While there is the zeration following from the ML.
Quote:I shall keep quiet and cool for a while, about the zeration business.
That is absolutely not necessary.