User blog comment:Sbiis Saibian/Introduction to Googology/@comment-168.212.150.41-20151110203629/@comment-5982810-20161020220021

I agree with you to some extent. One my Ultimate Large Number list, I actually have a number defined as lim(n-->oo) 1.1^^n. Informally we can think of this implying that 1.1^^inf is a finite number, but as LP9 pointed out really it's the limit that's defined. Plugging actual infinity into expressions is considered invalid.

But technicalities aside, all I was really saying was that if some part of your expression is undefined, then the entire expression is undefined. Thinking like a googologist is thinking like a programmer. A computer only understands explicit operations. It can not interpretted undefined expressions by definition because it can only understand what you program it to understand. For our purposes "infinity" is not a defined value, and so anything with it should not be considered defined either.