1. x<y<z: Yes, this is not needed and was added for "clarification". But it's not something I rely on so pls ignore.
2. assumption of n=2: Yes, thank you. I had initially rejected this idea for this very reason and then later reworked it because believed that I had been wrong.
It's the obvious errors that re really discouraging since it implies that I'm not always perceiving the same mathematical concepts in the same way - if that makes any sense at all.
I could have presented something more formal but I felt that would have been pretentious. I wanted it to sound conversational.
What I thought I was doing was showing how that 1 was divided over n dimensions. Except that once one accounted for the n=2 dimension, there was nothing left over for the rest. QED, yada, yada. Too bad I had to assume my conclusion in order to get there.
I don't know about further study. I already have 2 graduate degrees, they're just in other fields - obviously not math related. But I do love this little problem and playing with it so I hope to be back. I'll do something formal next time since that's preferred, even if I have reservations.