3 ms·
Can't we keep on applying the BB function i.e BB(BB(BB(...(BB(v)))) given that every application of BB still results in a finite number?
by rrampage 9y ago
Can't we keep on applying the BB function i.e BB(BB(BB(...(BB(v)))) given that every application of BB still results in a finite number?
- posterboy 9y agoyes, but "can" is rather optimistic. The largest number I saw written out is the number of symmetries in the monster group, spelled out on wikipedia (iirc).
- yters 9y agoYes, and you can generalize this to BBN(v, N), which means N applications of BB to v. If we replace N with v, it becomes a single parameter BBN(v). Then we can apply this thing to itself, and so on. So, with any finite storage space, we can represent an arbitrarily large number in this fashion. Thus, finite storage does not set an upper bound on the number that can be represented.