Bashicu matrix system: Difference between revisions
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subscripts are now actually subscripts. hopefully all of them.
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m (subscripts are now actually subscripts. hopefully all of them.) |
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- The parent of an entry x (a natural number in the array) is the last entry y before it in the same row, such that the entry directly above y (if it exists) is an ancestor of the entry above x, and y<x. The ancestors of an entry x are defined recursively as the parent of x and the ancestors of the parent of x.
- If A is empty, then A[n]=A for all natural numbers n. Otherwise let C be the last column of A, and let
- Say that an entry in
- A[n]=G+
For a long time, the problem of finding a proof of its well-orderedness was a famous problem in apeirology, but now the proof is finished.<ref>Source will be added as soon as it's public, which should be approximately 3 hours after this edit.</ref> The proof utilizes [[stability]], so the problem of finding a self-contained proof that BMS is well-ordered remains open for now. A related open problem is the well-orderedness of Y sequence, which is similar enough to BMS (below the limit of BMS) that it can be considered an extension.
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