04/23/2008, 11:44 AM

Wow, that was a very interesting post!

@GFR

I recognize that both the GML and ML as fundamental properties of hyperoperations. I also recognize that, although less intuitive, the Balanced Mother Law (BML) is very successful at producing the usual hyper1, hyper2, hyper3 as we know them. If you are responding to my comment in that thread, then I was only talking about BML, not the other two. I think so far we have established that the GML-hyper-0 is "zeration" as you define it, ML-hyper-0 is "succession" and BML-hyper-0 is the empty set.

On the subject of fuzzy feelings, I think you could play around with DL a little, because, as Kouznetsov's methods remind us, there is more than one way to get to infinity. You can go + or - or +i or -i, or even some other direction, and hopefully, if things are beautiful, then you should get to some fixed point of the previous hyperoperation. I personally think the sphere is the best way to visualize this. It is interesting to point out that many different fixed points can be obtained by changing the sign/direction of the infinity. For example, but which give the fixed points oo and 0 of multiples of a.

This makes me wonder if having a function such as would enumerate all fixed points of a[n-1]?

Andrew Robbins

@GFR

I recognize that both the GML and ML as fundamental properties of hyperoperations. I also recognize that, although less intuitive, the Balanced Mother Law (BML) is very successful at producing the usual hyper1, hyper2, hyper3 as we know them. If you are responding to my comment in that thread, then I was only talking about BML, not the other two. I think so far we have established that the GML-hyper-0 is "zeration" as you define it, ML-hyper-0 is "succession" and BML-hyper-0 is the empty set.

On the subject of fuzzy feelings, I think you could play around with DL a little, because, as Kouznetsov's methods remind us, there is more than one way to get to infinity. You can go + or - or +i or -i, or even some other direction, and hopefully, if things are beautiful, then you should get to some fixed point of the previous hyperoperation. I personally think the sphere is the best way to visualize this. It is interesting to point out that many different fixed points can be obtained by changing the sign/direction of the infinity. For example, but which give the fixed points oo and 0 of multiples of a.

This makes me wonder if having a function such as would enumerate all fixed points of a[n-1]?

Andrew Robbins