User blog comment:Bubby3/Hypothetical analysis of SAN second generation with BMS/@comment-35470197-20190406010732/@comment-24725252-20190406205610

I think that is a really deep-seated problem that we often have, which is not answereing the questions you give us. I seriously didn't think thoose questions were as important as you think it is. Because I didn't think you will stop taking my blog posts seriously when I ignore you, (often these are really hard questions that I'm not sure of right now), and often I forget about blog posts, which googolists often do. Sometimes I don't even you if you actually want an answer and not just asking a rhetorial question. Also, I think that you understood that you were thinking that I was, and I had to explain anything I left even a little bit ambigous.

1. Add \(\Omega\)'s to the OCF representation means if n is \(\psi(A)\), adding an (\Omega\)' to n results in \(\psi(A + \Omega)\), which means adding an (\Omega\) to the input of the outermost \(\psi\) function, and when we add an \(\Omega\), the ordinal is additievly principal meaning there is only one outermost psi. I thought that was perfectly clear, but to you I needed more clarification. Another question you asked is that why does that work, and that something from pair sequence doesn't necessarily continue into trio sequence. The reason is that in BM4, you search for the lowermost nonzero columm, so adding zeros to the bottom doesn't change it's behavior and (1,1,0) behaves no differently than (1,1), which is searching for first-row ancestors of itself which have a second columm of zero, then calls that the bad root. Because any columm between the rightmost columm and the bad root has an ancestor of the bad root, the bad root ascending rule doesn't change anything. Also, increasing the topmost row of all the columms of a terminal submatrix (a set of consective columms which includes the rightmost one) in which the bad root is contianed doesn't change it's behavor, so that's why (x,1,0) acts like (\Omega\) in OCF, until you get to the upgrade effect. Sorry for my misunderstanding.

2. I probally used Rathjen's standard OCF. I actually didn't think that clarifiying which specific ocf was as important as you claim. I thought people will assumed which OCF I was using based off context clues, and you will fill in the gaps, but that isn't ture. I'm not the only one who did this. Several people alsmo made alalysises of functions with an unspecified OCF, and you didn't complain because we didn't spcifiy the OCFS. I think that is just because BMS analysis are put under more scrunity than other analyses, or people are deciding that analyses must be formal. Either way, no one told me of this, and thank you for telling me I need to tell which specific OCF.

3. I essentially just paraphrased the definition of BMS, and I proved that the bad root ascending doesn't change anything in pair sequences. I didn't know that I had to give the exact definition of BM4 pair sequences for it to count, and I just thought that you will treat my definition as the same as the official definition. Also, I am going to either prove consistency with the original R function linear array (up to {0,{0}}), which nobody has doubted the consistency of, or I am going to do it with a slightly modified version of that function, which will make it easier.

4. To this question, I didn't think you seriously wanted to answer to that question, and were only asking a rhetroical question. So, to continue further we should go to z_(C_1(W)+1), g_(C_1(W)+1), etc. We hsould try to find the value of C_1(W+1) in relation to C_1(W). If that's not possible, we are limited to just above C_1(W) (in googological terms, only at this point), or we have to come up with radically new ways to expand on ordinals.

5. I fixed the mistakes you pointed out, and I didn't think I had to reply to the questions, in my mind, and I could just fix the problems, and they aren't worded as questions.

So, in general, it was me not thinking I had to answer them, or just thinking that there are no gaps in my analysis and that you will have no questions, and if you did, you would just have misinterepated my work. So, I am either try to clarify more things and have more details, and then try to answer your questions and then to take you seriously. This is so you actually take time to think about my blog posts and take them seriously, and take me seriiously, and you actually take time to ask questions if you have themm and think about my blog post.