User blog comment:P進大好きbot/New Googological Ruler/@comment-31580368-20190629142620/@comment-35470197-20190629225656

> As I wrote, it can be such functions as Loader's D or Hypcos's DAN (why by the way do you think that DAN is not well-defined?)

I did not say that DAN is ill-defined. I meant that DAN has never been proved to be well-defined.

Since you answered Laoder's number and DAN to my question "Do you know any specific candidates of large numbers which will be obviously between them?" , you must have formal proofs that they are between them. Please tell me the proofs.

Googologists sometimes state something like "the termination of BMS and DAN are obvious!" even though they do not have proofs. I hope that you are not such a googologist.

> Anyway, both my and your scale will be useless for beginners.

No. You are ignoring lower scales. When a beginner creates a large number approaximately \(f_{\omega^2}(10^{100})\), we usualy need to say "\(\omega^2\)" although beginners do not understand ordinals. Then the begginer is not able to understand the distance to well-known other large numbers.

Instead, we can tell that it is of level 7. Since I created the ruler to scale the distance to "the next step with valid examples", the beginner can intuitively understand the correct googological size. This is one of the aims of my ruler.

On the other hand, if you use your ill-defined ruler, no one has a benefit because there are at most two or three real examples between level 24 and 40.

Moreover, there will be no real examples between level 52 and 60, because all of them are completely ill-defined. Do you understand what PTO means? Do you understand that there are models of ZFC at which the functions have infinite loops under the assumption of the consistency of ZFC? Do you understand their pointwise well-definedness need \(\Sigma_1\)-consistency?