User blog comment:GdawgGamerTV/A New Number I thought of/@comment-35470197-20190106232311/@comment-35470197-20190110113307

1. Since few googologists here regard my issue as a serious one, I think that it is not suitable for me to edit the main article. It is not fair for me myself to do so before arguing with others.

Therefore what I should do is to announce the ill-definedness whenever I saw someone to state that BIG FOOT is well-defined. For this purpose, I wrote the blog post which I referred to above. Also, I wrote the existence of the issue at the talk page of "List of googolisms/Uncomputable numbers" |here. In addition, I constructed a new well-defined large number here which would be (non-naively) greater than any suspected well-defined replacements of BIG FOOT.

2. No. I just stated that Rayo's number is well-defined AS LONG AS one specifies the axiom. The issue is not so serious as BIG FOOT is, because there are many possible natural choices of axioms under which Rayo's number is well-defined unlike BIG FOOT. (I note that Rayo himself did not specify the axiom, and hence the problem is a little sensitive.)

Also, some googologists might state that the axiom should be the ZFC ones, because it is omitted. (Traditionally, omitted axioms should be regarded as the ZFC ones.) I denied this opinion in my blog post, because Rayo's number is not definable under the ZFC axioms.