User blog comment:Eners49/The secret 0th hyper-operator?/@comment-35470197-20180726231426/@comment-2601:142:2:EC49:5CB6:1626:ABFF:B911-20180731143122

@MilkyWay90 Yeah, you're right, we should probably get back on topic, but we've pretty much exhausted everything we can say about the 0th hyper-operator, so i'm just gonna use this comment to talk about a few ideas I had.

Idea #1: SO. Fandom users can't make blog posts, BUT they can comment, (As evidenced by how you're reading this.) So what if somebody like @MilkyWay90 or @Eners49 (Or really anybody who has a wikia account) made a blog post where fandom users can comment googology ideas they have like these ideas that I'm commenting!

Idea #2: So this is an ordinal notation I call "Double Ordinal Array Notation" or DOAN for short. There's like a 95% chance somebody else came up with it before me. It's definied first with arrays like so:

(0,0) = 0

(0,1) = 1

(0,2) = 2

(0,n) = n

(1,0) = 0

(1,1) = \(omega\)

(1,2) = \(omega\) times 2

(1,n) = \(omega\) times n

(2,n) = \(omega\) to the power of n

(3,n) = \(omega\) tetrated to the n

etc.

This is pretty strong, (4,1) is already equal to epsilon 0, but it skips over a LOT of ordinals. But there's more to DOAN than just this. There are also ARRAY ARRAYS!

{(w,x),(y,z)} = (w,x) + (y,z)

{(a,b),(w,x),(y,z)} = (a,b) + (w,x) + (y,z)

And you have to put larger ordinals before the smaller ones.

{(0,2),(1,1)} NOT VALID.

{(1,1),(0,2)} VALID.

Pretty simple, but it allows you to write all ordinals below omega squared! And maybe all ordinals up to omega cubed too, but don't qoute me on that last one. However, We STILL aren't done with DOAN yet, there're still ADVANCED ARRAY ARRAYS.

{(1,1),(0,2)} = \(omega\) + 2

{(1,1),,(0,2)} = \(omega\) * 2

{(1,1),,,(0,2)} = \(omega\) ^ 2

Once again, don't quote me on this, but I think EVERY ORDINAL UP TO ((1,1)(1,1)) (Not {(1,1),(1,1)} that's just omega times 2. this is OMEGA COMMA OMEGA) CAN BE WRITTEN IN ADVANCED ARRAY ARRAY FORMAT.

I had an idea 3 but this comment is already an essay.