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W@, or WAt (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 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 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 aâ€¦
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https://sites.google.com/site/numbersitetma/home
It's highly in the works, mostly because I'm learning google sites by making this site. Obviously I won't be making any articles based off of what I'm posting on this site (but I will help if any articles are made for some reason).
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And did something absolutely stupid! I defined a thing.
It's the "dipsi" function, Î¨Ïˆ(n). Simply put, Î¨Ïˆ(n) is the largest number definable within n standard universes, assuming a "standard universe" has a volume the same as the observable universe, and each symbol takes up 1 planck cube of volume. Note that it is different from RAYO(n * 9.475 * 10^184). Note that this excludes dipsi and higher variants (and anything defined by it or its higher variants), but not anything else similar, like RAYO(n). RAYO(n) and similar are fair game.
But dipsi is beaten by tripsi, which is defined as dipsi nested n times, with n being the n of the innermost dipsi; it's Î¨ÏˆÏˆ(n). Î¨ÏˆÏˆ(2) is... decent, to say the least, being Î¨Ïˆ(Î¨Ïˆ(2)).
Nesting tripsi the same wayâ€¦
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I decided to dabble in hyperfactorials for a change and, well, first off, 5 tetrafactorial is pretty big. Approximately E2.188#(E3.339#4). I approximated this as E3#4#2, although I'm not sure if this is as accurate as is attainable. It's pretty close, though, I think.
I'm also working on approximating 6 tetrafactorial and 7 tetrafactorial. Googologically speaking, tetrafactorials are pretty weak, but pretty interesting, too.
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I've been taking BEAF in an entirely different direction than multidimensional arrays. Much like those, these are technically just linear arrays of monstrous length (the number of entries itself being highly googological). Only these stay more or less linear themselves.
At the heart of CBEAF is a simple array, âŸ¨a,bâŸ©. It has a simple definition; âŸ¨a,bâŸ© = {a,a,a...a,a,a} with b a's. When it has more than 2 arguments, it follows BEAF's rules. Functions of this kind are called "Class A" for brevity's sake; when they have two arguments, a and b, they define the function a level below it with b a's. A level above âŸ¨a,bâŸ© is ï½¢a,bï½£, and above that is â¸¤a,bâ¸¥. â¸¤a,bâ¸¥ can be generalized as :a,b:, and anything above it in level with multiples of colons (::aâ€¦
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