User blog comment:TheGoogologist/Hunt for the Largest Number: Part 1/@comment-38468997-20190310100806/@comment-35470197-20190310110033

> even BIG FOOT is ill-defined, the notation itself even says FOOT^(10^100)

I said that (not only BIG FOOT but also) FOOT is ill-defined.

> what's the defenition of FOOT?

You should know it because you used it.

> the only thing you can do, is to combine functions.

It is good to learn the notion of a definable class function, which gives you a way to define a function in a direct way. It is helpful for you to understand uncomputable functions.

> I completely understand the FOOT function

Then you have understood the reason why it is ill-defined. Formalising \(\alpha_0\) in the definition of FOOT includes the ovbious contradiction \(\textrm{Ord}^{V_{\textrm{Ord}}} = \textrm{Ord}\).