User blog comment:Edwin Shade/A Complete Analysis of Taranovsky's Notation/@comment-30118230-20180201150715/@comment-32876686-20180201152908

By using the Bashicu-Matrix System and other ordinal notations whose limits are not known, I hope at least one of these will supercede Taranovsky's notation in strength and therefore define the limit of TON in terms of another notation, which I'm assuming is what is meant by "finding the limits of Taranovsky's ordinal notation".

Still though, given that so far only TON appears to be able to express it's own strength, why can we not consider the simple statement: "the limit of TON is \(C(C(C(...C(\Omega_n,0)...,0),0),0)\)" as a valid "proof" of the limit of TON, and therefore do away with all statements of the sort "the limit of TON is unknown" ?