Hey, Sheldon
I had written a page long reply to what you just said; but somehow my computer deleted it and it didn't post (I don't know what happened there). I'm a little upset because I had written a fair amount of math, but in the meantime I'll give you the rundown. I am absolutely certain I can prove that this tetration is \( C^\infty \) (I went on to relay how this is really no different than the construction of \( \phi \) using infinite compositions). However, I can't quite prove it for hyper-operations; and I'm trying to abstract how I can do it for tetration, so that it works for pentation and the sort.
So I don't have an essay-like proof for \( C^{\infty} \) nature of \( \text{tet}_\phi \). But trust me; it's not much more than the construction of \( \phi \). Just a whole load of infinite composition stuff. And I'm busy on generalizing the proof so it works for pentation, hexation, etc...
Give me a couple weeks. I'm going to pull more all nighters than I should, and I'll have this.
Like how every presidential secretary should respond--give me a week and I'll circle back to your question.
Regards, James
We'll circle back.
EDIT: I also had written about how a perl script won't fix your problems. This forum needs to run on MathJax. Which is the javascript version of LaTeX. For god's sakes Henryk.
Lol.
I had written a page long reply to what you just said; but somehow my computer deleted it and it didn't post (I don't know what happened there). I'm a little upset because I had written a fair amount of math, but in the meantime I'll give you the rundown. I am absolutely certain I can prove that this tetration is \( C^\infty \) (I went on to relay how this is really no different than the construction of \( \phi \) using infinite compositions). However, I can't quite prove it for hyper-operations; and I'm trying to abstract how I can do it for tetration, so that it works for pentation and the sort.
So I don't have an essay-like proof for \( C^{\infty} \) nature of \( \text{tet}_\phi \). But trust me; it's not much more than the construction of \( \phi \). Just a whole load of infinite composition stuff. And I'm busy on generalizing the proof so it works for pentation, hexation, etc...
Give me a couple weeks. I'm going to pull more all nighters than I should, and I'll have this.
Like how every presidential secretary should respond--give me a week and I'll circle back to your question.
Regards, James
We'll circle back.
EDIT: I also had written about how a perl script won't fix your problems. This forum needs to run on MathJax. Which is the javascript version of LaTeX. For god's sakes Henryk.
Lol.
