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What happens if you take the larger of a and b and run all the Turing machines for that many steps?

Among all possible values of BB(n) for some fixed n, it's the smallest such value that is the true value.

The issue is that there is no way within ZFC to determine which value is the smallest.

What are a and b?

Does it matter? My reading is basically "if you have two distinct candidates, isn't that a way to always disprove at least one of them?"