REXN

WIIIIIIIIIIIIIII.........IIIIIIIIIIIIIIIIIIIIIP

Stands for RomaronzoTHEThingy's Exploding X Notation

f(0) = 0

f(1) = 1

f(a) = f(a-1)+f(a-2)

f(a,2) = f

a

{\displaystyle ^a}

(a)

f(a,3) is more iteration...

etc...

f(a,1,2) = if f(a,a) = ƒ(a) then f(a,1,2) =

f
a

(
a
)

{\displaystyle f^a(a)}

etc.

FINALLY STARTING...

X(a) = f(a,a,a...a,a,a) a times

X(a) ≈

f

ω
ω

(
a
)

{\displaystyle f\_{\omega^\omega}(a)}

X(a,2) = X

a

{\displaystyle ^a}

(a)

X(a,2) ≈

f

ω
ω

1

(
a
)

{\displaystyle f\_{\omega^\omega+1}(a)}

etc...

X(a<1>b) = X(a,a,a...a,a,a) b times

X(a<1>a) ≈

f

ω
ω

2

(
a
)

{\displaystyle f\_{\omega^\omega2}(a)}

X(a,2<1>b) = X(a<1>X(a<1>X(a<1>...a)))...))) b times

X(a,2<1>a) ≈

f

ω
ω

2
1

(
a
)

{\displaystyle f\_{\omega^\omega2+1}(a)}

etc.

X(a<1>b,2) = X(a,a,a...a,a,a<1>a) b times

X(a<1>b,2) ≈

f

ω
ω

3

(
a
)

{\displaystyle f\_{\omega^\omega3}(a)}

etc.

X(a<1>b<1>c) = X(a<1>b,b,b...b,b,b) c times

X(a<1>a<1>a) ≈

f

ω

ω
2

(
a
)

{\displaystyle f\_{\omega^{\omega2}}(a)}

etc.

X(a<1>\*b) = X(a<1>a<1>a<1>a...a<1>a<1>a<1>a) b times

X(a<1>\*a) ≈

f

ω

ω
2

(
a
)

{\displaystyle f\_{\omega^{\omega^2}}(a)}

etc.

X(a<1>\*\*b) = X(a<1>\*a<1>a<1>a<1>a...a<1>a<1>a<1>a) b times

X(a<1>\*\*a) ≈

f

ω

ω
2

2

(
a
)

{\displaystyle f\_{\omega^{\omega^2}2}(a)}

X(a<1><1>b) = X(a<1>\*\*\*...\*\*\*a)

X(a<1><1>a) ≈

f

ω

ω
2

2

(
a
)

{\displaystyle f\_{\omega^{\omega^22}}(a)}

etc.

NOTE: X(a<1><1>b) = X(a<1><1>a<1><1>a<1><1>...)

X(a<2>b) = X(a<1><1><1>...<1><1><1>a) b times

X(a<2>a) ≈

f

ω

ω
3

(
a
)

{\displaystyle f\_{\omega^{\omega^3}}(a)}

etc.

X(a<<1>>b) = X(a<a<a...<a<a<a>a>a>a...>a>a>a) b times

X(a<<1>>a) ≈

f

ω

ω
ω

2

(
a
)

{\displaystyle f\_{\omega^{\omega^\omega2}}(a)}

etc.

X(a#b) = X(a<<<...<<<1>>>...>>>a) b times

X(a#b) ≈

f

ω

ω

ω
2

(
a
)

{\displaystyle f\_{\omega^{\omega^{\omega^2}}}(a)}

etc.

~~X(a##b) = X(a#a#a...a#a#a) b times~~

UPDATE: do all the stuff to # first.

X(a##b) ≈

f

ω

ω

ω
2

2

(
a
)

{\displaystyle f\_{\omega^{\omega^{\omega^2}2}}(a)}

etc.

X(a#<1>#b) = X(a###...###a) b times

X(a#<1>#b) ≈

f

ω

ω

ω
2

1

(
a
)

{\displaystyle f\_{\omega^{\omega^{\omega^2+1}}}(a)}

X(a##<1>#b) is like normal.

etc.

X(a#[1]#b) = X(a#b)

X(a#[2]#b) = X(a#<<<...<<<1>>>...>>>#a) b times

X(a##[2]#b)

etc.

etc.

X(a#[[1]]#b) = X(a#[#[#[...#[#[#]#]#]#..]#]#]#a) b times

etc.

X(a~1) = X(a#a)

X(a~2) = X(a#[[[...[[[1]]]...]]]#a) a times

etc.

X(a~~b) = X(a~a~a...a~a~a) b times

etc.

WIP!

## Numbers

Xol = X(100)

Xolplex = X(X(100))

Duxol = X(100,2)

Trixol = X(100,3)

Tetraxol = X(100,4)

etc.

Xeol = X(10,100)

Xeolplex = X(10,X(10,100))

Unduypaxol = X(100,1,2)

"unduyp" is like from my other notation's numbers.

so continue...

Xeolid = X(10,100,2)

Xeolitri = X(10,100,3)

Xeolitet = X(10,100,4)

etc.

Deol = X(10,10,100)

Deolid = X(10,10,100,2)

etc.

Treol = X(10,10,10,100)

Tetreol = X(10,10,10,10,100)

etc.

Xeoxes = X(10<1>100)

Xeoxesid = X(10,2<1>100)

etc.

Deoxes = X(10,10<1>100)

etc.

Xeoxesod = X(10<1>100,2)

Xeoxesodid = X(10,2<1>100,2)

etc.

Deol-oa-xeoxes = X(10<1>10,100)

Deol-oa-xeoxes-id = X(10,2<1>10,100)

etc.

Deol-oa-xeoxes-od-id = X(10,2<1>10,100,2)

etc.

Xeoxes-oa-xeoxes = X(10<1>10<1>100)

etc.

Astral-xeoxes = X(10<1>\*100)

etc.

Double-astral-xeoxes = X(10<1>\*\*100)

Triple-astral-xeoxes = X(10<1>\*\*\*100)

Quadruple-astral-xeoxes = X(10<1>\*\*\*\*100)

etc.

Xeoxesad = X(10<1><1>100)

etc.

Xeoxesatri = X(10<1><1><1>100)

etc.

Xeodes = X(10<2>100)

etc.

Xeotres = X(10<3>100)

Xeotetres = X(10<4>100)

etc.

Xiatol = X(10<100>10)

Xeol-ej-xiatol = X(10<10,100>10)

etc.

Xiatol-ej-xiatol = X(10<10<100>10>10)

etc.

Duxalax = X(10<<1>>100)

etc.

Trixalax = X(10<<<1>>>100)

Tetraxalax = X(10<<<<1>>>>100)

etc.

Hyperaxalax = X(10#100)

etc.

Diaperaxalax = X(10##100)

Triaperaxalax = X(10###100)

Tetriaperaxalax = X(10####100)

etc.

Xeoxes-pa-joralania = X(10#<1>#100)

etc.

Duixeex = X(10#[2]#100)

etc.

Triixeex = X(10#[3]#100)

Tetraixeex = X(10#[4]#100)

Xeexulus = X(10#[100]#10)

etc.

Xeol-uy-xeexulus = X(10#[10,100]#10)

etc.

Xeedulus = X(10#[[1]]#100)

Xeetrulus = X(10#[[[1]]]#100)

Xeetetrulus = X(10#[[[[1]]]]#100)

etc.

Xoonold = X(100~2)

Xoonoltri = X(100~3)

Xoonoltet = X(100~4)

etc.

Xoonwiol = X(10~100)

etc.

Xeol-gi-xoonwiol = X(10~10,100)

etc.

Xoonwiol-gi-xoonwiol = X(10~10~100)

etc.

Doonwiol = X(10~~100)

etc.

Troonwiol = X(10~~~100)

Tetroonwiol = X(10~~~~100)

etc.

Goowixol = X(10~~~...~~~10) 100 times

WIP!