User blog comment:Alemagno12/googology 4 dummies/@comment-32876686-20180128035641

Here are my thoughts to these rules.

"1. Don't try to create the largest number ever. Yet."

I agree completely - as you'll note the tendency of an individual to claim their number as the "largest" is inversely proportional to the actual size of their number.

"2. Don't use Infinity anywhere in your number/notation/etc."

Infinity isn't necessarily a bad thing, as demonstrated by the use of the fast-growing hierarchy to enlist transfinites to produce finites, but when people claim infinity as a largest number it is clearly missing the point of Googology.

"3. Make sure that, if you're making a notation or anything that uses that notation, it's well-defined."

Once more I agree. If you wanted to be more specific however, you could say that a notation is "well-defined" if and only if anyone with sufficient math skills could calculate any well-formed expression in your notation and arrive at the same result anyone else would come to. Defining a function with ordinals that do not possess fundamental sequences would be an "ill-defined" notation because different people could create their own system of fundamental sequences; but utilizing a notation with a clearly defined system of fundamental sequences would be well-defined.

"4. Finally, the most important rule of all, always zoom out."

Or in alternative words, always look outside the box and think of a way to transcend all that you've done before. Learning about ordinals is a very useful way to understand the art of diagonalization, as you are continually reaching and breaking limits in what is just another diagonalizable system which is contained in yet another system, and ad infinitum.