User blog comment:Eners49/New Notation Idea?/@comment-2601:142:2:EC49:84E3:14C4:34DB:5371-20180623154511

I don't know how ordinals work, but i'm gonna put my two cents about how big this is. WARNING. Essay ahead. (inhale)

Your [n] seems equal in size to 4n (see Introduction to BEAF), which is decently strong, so props to you.

"What about multiple bracket sets then?" You might ask. "are they considerably stronger?" Well let's make a weaker function than [x, y] so we can see how freaking MASSIVE [x, y] is. This new, weaker function (x, y) is equal to x with y sets of brackets around it (so (3, 3) would be equal to [3].)

This definition would make (x, y) equal to 4x (again, see Introduction to BEAF) which is just STUPIDLY big, as the amount of time it would take just to get 4x down to single brackets would be ASTRONOMICAL.

Now, (at long last.) for [x, y]. With our newfound knowledge of (x, y), we can see that [x, y] is equal to 4x Well done! You've created a function so strong that even the middle number is UNIMAGINABLY huge!

"But hold on!" You say. "That Introduction to BEAF article you mentioned also talks about functions far stronger than double curly brackets! What about triple curly brackets? Or even QUADRUPLE curly brackets?" Good question! It turns out that triple curly brackets completely dwarf [x, y], and I'm too tired now to try to figure out [x, y, z].

Continuation tomorrow. Let me know if this makes zero sense, and I'll try to clarify.