FANDOM


Untitled Notation might be one of the first notations i ever made. When i discovered googology, i couldn't understand BEAF, so i tried to make simpler notations to beat it. For example, i made my EUAN (old) when trying to extend ExE (which i didn't understand well at that point).

But this time, i'm gonna make a general definition for Untitled notation.

# is any valid expression.

& is any structure of -'s

Basic

a-b-c = a{c}b

Multiple entries

#-n-m = #-(#-(...#-(#-(#-n)))) with m levels

Multiple Bars

#---...---n (m bars) = #---...--n---...--n---...--n ... ---...--n---...--n---...--n with n entries and m-1 bars

Exponentiation

#---...---n (m bars) = #-*-*-*...*-*-*-n (m bars)

#&*-n = #&n&n&n...n&n&n with n entries

#&^(&*-)n = #&^&*&^&*&^&*...*&^&*&^&*&^&n with n levels

#-^-n = #-*-*-*...*-*-*n with  n levels

Tetration and beyond

#&^^^...^^^(&*-)n (m carats) = #(&^^^...^^^&)^^^...^^(&^^^...^^^&)^^^...^^(&^^^...^^^&)...(&^^^...^^^&)^^^...^^(&^^^...^^^&)^^^...^^(&^^^...^^^&)n with m-1 carats between (&^^^...^^^&)'s and n (&^^^...^^^&)'s

#-^^^...^^^-n = #-^^^...^^-^^^...^^-^^^...^^-^^^...^^-...^^^...^^-^^^...^^-^^^...^^-n with n levels

Extended Arrow Notation I

-- UNDER CONSTRUCTION --

FGH

Untitled Notation FGH Ordinals
a-b-c  \omega
a-b-c-d  \omega +1
a-b-c-d-e  \omega +2
a--b  \omega 2
a--b-c  \omega 2 + 1
a--b-c-d  \omega 2 + 2
a--b--c  \omega 3
a---b \omega^2
a---b-c \omega^2+1
a---b--c \omega^2+\omega
a---b---c

\omega^22

a----b \omega^3
a----b----c \omega^32
a-----b \omega^4
a------b \omega^5
a-^-b \omega^{\omega}
a-^-b-^-c \omega^{\omega}2
a-^-*-b \omega^{\omega+1}
a-^-*-*-b \omega^{\omega+2}
a-^-*-^-b \omega^{\omega2}
a-^-*-^-*-b \omega^{\omega2+1}
a-^-*-^-*-^-b \omega^{\omega3}
a-^--b \omega^{\omega^2}
a-^--*-b \omega^{\omega^2+1}
a-^--*-^-b \omega^{\omega^2+\omega}
a-^--*-^-*-^-b \omega^{\omega^2+\omega2}
a-^--*-^--b

\omega^{\omega^22}

a-^---b \omega^{\omega^3}
a-^---*-^---b \omega^{\omega^32}
a-^----b \omega^{\omega^4}
a-^-^-b \omega^{\omega^{\omega}}
a-^-^-*-^-^-b \omega^{\omega^{\omega}2}
a-^(-^-*-)b \omega^{\omega^{\omega+1}}
a-^(-^-*-^-)b \omega^{\omega^{\omega2}}
a-^-^--b \omega^{\omega^{\omega^2}}
a-^-^---b \omega^{\omega^{\omega^3}}
a-^-^-^-b \omega^{\omega^{\omega^{\omega}}}
a-^-^-^--b \omega^{\omega^{\omega^{\omega^2}}}
a-^-^-^-^-b \omega^{\omega^{\omega^{\omega^{\omega}}}}
a-^-^-^-^-^-b \omega^{\omega^{\omega^{\omega^{\omega^{\omega}}}}}
a-^^-b \omega^{\Omega}
a-^^-*-b \omega^{\Omega+1}
a-^^-*-^-b \omega^{\Omega+\omega}
a-^^-*-^-^-b \omega^{\Omega+\omega^{\omega}}
a-^^-*-^^-b \omega^{\Omega+\omega^{\Omega}}
a-^^-*-^^-*-^^-b \omega^{\Omega+\omega^{\Omega}2}
a(-^^-)^-b \omega^{\Omega+\omega^{\Omega+1}}
a(-^^-)^-*(-^^-)^-b \omega^{\Omega+\omega^{\Omega+1}2}
a(-^^-)^--b \omega^{\Omega+\omega^{\Omega+2}}
a(-^^-)^-^-b \omega^{\Omega+\omega^{\Omega+\omega}}
a(-^^-)^-^-^-b \omega^{\Omega+\omega^{\Omega+\omega^{\omega}}}
a(-^^-)^-^^-b \omega^{\Omega+\omega^{\Omega+\omega^{\Omega}}}
a(-^^-)^(-^^-)^-^-b \omega^{\Omega+\omega^{\Omega+\omega^{\Omega+\omega}}}
a(-^^-)^(-^^-)^-^^-b \omega^{\Omega+\omega^{\Omega+\omega^{\Omega+\omega^{\Omega}}}}
a(-^^-)^(-^^-)^(-^^-)^-^^-b \omega^{\Omega+\omega^{\Omega+\omega^{\Omega+\omega^{\Omega+\omega^{\Omega}}}}}
a-^^--b \omega^{\Omega2}
a-^^--*-^-b \omega^{\Omega2+\omega}
a-^^--*-^^-b \omega^{\Omega2+\omega^{\Omega}}

a-^^--*(-^^-)^-^^-b

\omega^{\Omega2+\omega^{\Omega+\omega^{\Omega}}}
a-^^--*-^^-- \omega^{\Omega2+\omega^{\Omega2}}
a(-^^--)^-^^-b \omega^{\Omega2+\omega^{\Omega2+\omega^{\Omega}}}
a(-^^--)^-^^--b \omega^{\Omega2+\omega^{\Omega2+\omega^{\Omega2}}}
a(-^^--)^(-^--)^-^--b \omega^{\Omega2+\omega^{\Omega2+\omega^{\Omega2+\omega^{\Omega2}}}}
a-^^---b \omega^{\Omega3}
a-^^---*-^^-b \omega^{\Omega3+\omega^{\Omega}}
a-^^---*-^^--b \omega^{\Omega3+\omega^{\Omega2}}
a-^^---*-^^---b \omega^{\Omega3+\omega^{\Omega3}}
a(-^^---)^-^^--b \omega^{\Omega3+\omega^{\Omega3+\omega^{\Omega2}}}
a(-^^---)^-^^---b \omega^{\Omega3+\omega^{\Omega3+\omega^{\Omega3}}}
a(-^^---)^(-^^---)^-^^---b \omega^{\Omega3+\omega^{\Omega3+\omega^{\Omega3+\omega^{\Omega3}}}}
a-^^---- \omega^{\Omega4}
a-^^----*-^^---b \omega^{\Omega4+\omega^{\Omega3}}
a-^^----*-^^----b \omega^{\Omega4+\omega^{\Omega4}}
a(-^^----)^-^^----b \omega^{\Omega4+\omega^{\Omega4+\omega^{\Omega4}}}
a-^^-----b \omega^{\Omega5}
a-^^-----*-^^-----b \omega^{\Omega5+\omega^{\Omega5}}
a-^^------b \omega^{\Omega6}
a-^^-------b \omega^{\Omega7}
a-^^-^-b \omega^{\Omega\omega}
a-^^-^-*-^^-^-b \omega^{\Omega\omega+\omega^{\Omega\omega}}
a-^^(-^-*-)b \omega^{\Omega(\omega+1)}
a-^^(-^*-^-)b \omega^{\Omega(\omega2)}
a-^^-^--b \omega^{\Omega\omega^2}
a-^^-^-^-b \omega^{\Omega\omega^{\omega}}
a-^^-^^-b \omega^{\Omega\omega^{\Omega}}
a-^^-(-^^-*-^^-)b \omega^{\Omega\omega^{\Omega+\omega^{\Omega}}}
a-^^-^^--b \omega^{\Omega\omega^{\Omega2}}
a-^^-^^---b \omega^{\Omega\omega^{\Omega3}}
a-^^-^^-^-b \omega^{\Omega\omega^{\Omega\omega}}
a-^^-^^-^^-b \omega^{\Omega\omega^{\Omega\omega^{\Omega}}}
a-^^-^^-^^--b \omega^{\Omega\omega^{\Omega\omega^{\Omega2}}}
a-^^-^^-^^-^-b \omega^{\Omega\omega^{\Omega\omega^{\Omega\omega}}}
a-^^-^^-^^-^^-b \omega^{\Omega\omega^{\Omega\omega^{\Omega\omega^{\Omega}}}}
a-^^-^^-^^-^^-^^-b \omega^{\Omega\omega^{\Omega\omega^{\Omega\omega^{\Omega\omega^{\Omega}}}}}
a-^^^-b \omega^{\Omega^2}
a-^^^-*-^^^-b \omega^{\Omega^2+\omega^{\Omega^2}}
a(-^^^-)^^-b \omega^{\Omega^2+\Omega}
a(-^^^-)^^--b \omega^{\Omega^2+\Omega2}
a(-^^^-)^^-^-b \omega^{\Omega^2+\Omega\omega}


-- UNDER CONSTRUCTION --

About \Omega Ordinals

\omega^{\Omega} = \sup(\omega,\omega^{\omega},\omega^{\omega^{\omega}},...)

\#\Omega = \sup(\#, \#\#, \#\#\#,...)

--- UNDER CONSTRUCTION ---

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