User blog comment:PsiCubed2/My own version of BMS/@comment-35470197-20181120231600/@comment-35470197-20181122112553

> Refusing to actually state your own definition in plain English while hiding behind vague statements like "my version is compatible with BM2" is also dishonest.

I could not understand why you can say such a thing. It is more dishonest to state that you can write a shorter proof than mine with your unwritten "pretty good intuitive idea" and "a pretty straight-forward argument" before you actually start writing.

Stating that you can write a proof better than me before writing is absolutely rude.

In addtion, do you remember? When I wrote that I verified in my mind, you doubted me as if I showed the termination of BM1 with infinite loops. When you asked me BM4 rule set, you wrote that you are not interested in my proof. I could not understand why I should write an additional expanation for such a person. Maybe you would not even take a look at it.

Anyway, how many days you will spend to write it? Since it is so pretty good. will you write it in a month?

> The only thing I've done here is to fix the original notation by adding a small modification. I guess I should take credit for coming up with such a simple fix, but that's a small achievement compared to what Bashicu has already done.

I disagree with it. If your definition actually works better beyond pair sequences, then it is far from a small achievement, At least, I will regard it as your own great contribution.

> Have you even bothered to read my blog post? It's all written write right there!

It is not what I am asking. If you actually had a straight-forward way to prove the termination by a pretty good 1-to-1 correspodence \(t\) between your own version in your blog post and the Buchholz system, I would like you to ask an explicit way to describe \(t(M[n])\) by using \(t(M)\) for a pair sequence \(M\). Since it is not so simple, I doubt that you do not know it at all.

Again, please answer. Do you have a way to describe \(t(M[n])\) by using \(t(M)\)? If not, then I doubt that you actually have a valid idea to prove the termination using Buchholz's ordinal notation system. Or as anoother googologist did, you might just have an idea "pair sequence is similar to Buchholz's ordinal notation system!"