Comment by bo1024
8 months ago
The point is that when it "never stops", there are models of ZFC in which the "infinity" number of steps it runs for isn't considered infinity by the model, it's a made-up "nonstandard" number that is smaller than infinity but larger than any integer. And that model considers that to be "halting", so that model says the TM halts.
That’s just a change of definition. That isn’t really saying that BB(748) is different under a different model, just that there’s a BB’ equivalent for that model and BB’(748) is equal to something else.