Hi,

In slide 3 we say that given n' there is a m'. Why is this true? Does it have to do with the bounded busy beaver problem which says that there is a BB(n')?

If yes, in the BB problem we are talking about TMs with a specific tape dictionary {0,1}, here we do not restrict the tape dictionary, so why is it still correct?

Also, in the case of bounded busy beaver we said that this function is computable because we can use the constants BB(n) for each n until the bound. How do we know that BB(n) indeed exists for each bounded n? Or we assume that we don't know, but for each n that is defined we could build our TM to calculate it?

Thanks!