User blog:TheMostAwesomer/W-@ Notation

W-@, or W-At (or just Wat) is something I've done. CBEAF got too unwieldy for the time being, so I changed over to a new project. W-@ is quite a bit simpler, but still gives decently large numbers anyway.

Level 1
Level 1 of W-@, or simply W-@ Notation, is defined as follows:

Wn@m = n^^^...^^^n w/ m ^'s (I'm only using ... because I'm bad at the wiki's math system), if n and m are both natural numbers. Level 1 doesn't need any other rules, as this one completely covers them (if n = 1, it always would solve to 1, and if m is 1, it's n^n, both obvious from the rule given). It's essentually {n,n,m} in BEAF.

Level 2
Level 2 of W-@ is Extended W-@ Notation. It permits an arbitrary amount of @s. The generalized rules for x>2 are...

Wn@^xm (that is, x @s, x is also a natural number) = W(Wn@^x(m-1)@^x(m-1)

Wn@^x1 = Wn@^(x-1)n

When x = 2,

Wn@@m = W(Wn@@m-1)@@m-1

Wn@@1 = Wn@n

Even Wn@@m makes decently large numbers.

When x = 1, it's just W-@ Notation.

Level 3
Level 3 of W-@ is Extended Extended W-@ Notation, or Super-Extended W-@ Notation. The lowest form of Super-Extended W-@ is Wn@#m, which follows its own slightly different ruleset. The generalized rules for x>1 are...

Wn@^x#m = W(Wn@^x#m-1)@^x#m-1

Wn@^x#1 = Wn@^(x-1)#n

For x = 1,

Wn@#m = W(Wn@^mn)@#m-1

Wn@#1 = Wn@^nn

I get bored often.