My question is this What is the least upper bound ordinal of my linear n-symbol partition ordinal?
I am self-learning person. I create the ordinal sequence that I can't prove it mathematically.
I know the fundamental step by step method of how to increase my ordinal to any higher ordinal but I don't know how to write it down mathematically. The the fundamental step by step is like an axiom which is taken to be true. The problem is as the ordinal get larger, the fundamental step by step will be longer to work up to the higher ordinal. At some point, it will take too long time to do.
I try fix this by looking for the pattern can create some formula to make larger step. But the problem is that the formula is totally based on the observation which isn't proved to be correct. However, I can't find any example that make the formula incorrect at all. What should I do ? Should I keep using it ?
Another problem is that I don't know how to prove those formula because it is the formula in my ordinal which appear to be different from the normal mathematical for me. Also it might be because of that my question is too hard for me or probably beyond my knowledge. If it is really beyond my knowledge, what should I do ? Which knowledge I have to learn it understand my ordinal ?