User blog comment:Googleaarex/Bashicu Matrix System Analysis (Part 1)/@comment-27516045-20170725132813/@comment-5529393-20170730115619

@PsiCubed2

We don't need to worry about SAN not having fundamental sequences because we already have a version that does. My idea was to make an equivalent definition that was defined differently, under the hope that it could be simpler and conceptually more intuitive.

I disagree about SAN being inherently complicated; the methodology for how he keeps extending his notation, at least through Dropper Array Notation (which is about as far as I have even somewhat grokked) seems clear and straightforward.

Basically, you start with Nested Array Notation, which is just like other nested array notations, where you have entries divided by "separators". This runs out at epsilon_0, so we add the symbol `, which is a "1-separator", which is a separator within separators; this allows us to create more separators. Then when that runs out, you add the double comma, which is a 2-separator, or a separator within 1-separators. (The symbol ' becomes {1,,2}) This allows us to create stronger 1-separators, which allows us to create stronger basic separators, which allows us to create stronger notations. Then we add the triple comma as the first 3-separator, and so on. So it's somewhat akin to creating stronger and stronger diagonalizers in OCFs.

So I feel like the intuitive notion of Dropper Array Notation is pretty straightforward, and so there could be a much simpler way to define it formally.

@Kyodaisuu

Thanks, I'll try to decipher it!