User blog:SuperSpruce/Alternate extension to BEAF arrays past Tetrational arrays

Yes, I know Birds Array Notation gives an alternate to BEAF, but this is what I have come up with independently.

This notation uses minus signs as the special separator. This notation will probably be extended to have plus signs, asterisks, etc. Plus signs used in these formulas are USED NORMALLY as addition.

For convenience sake we will sometimes only be concerning what happens inside the separator, notated in parenthesis.

(((...((0)1)...)1)1)=(1-) ε_0

(b-)(b-)(b-)...(b-)(b-)=(1,b-) (ε_0)^ω if b=1

(a,b-)(a,b-)...(a,b-)=(a+1,b-)

Yada, yada, yada. Just do what you would normally do in tetrational arrays until...

((((...((0)1)...)1)1),b-)=([b+1]-) (ε_0)^((ε_0)b)

b can become an array as well! It can be a tetrational array, which can be converted into minus notation, and rinse and repeat.

((1-)-) (ε_0)^(ε_0)^2

(((...((1-)-)...)-)-)=(1-,1) (ε_0)^(ε_0)^ω (((...((1-,a)-,a)...)-,a)-,a)=(1-,[a-1]), the a-1 is NORMAL SUBTRACTION.

The a can become an array as well, and even a minus notation.

(1-,1-) (ε_0)^^3

The second minus can nest and make an entry after it just like it did with the first minus.

(1-,1-,1-,...,1-,1-)=(1-1) THIS IS NOT SUBTRACTION. (1-1) IS NOT (0). ε_1

I’ll continue/extend this later.