FANDOM


Untitled Notation (Factorial Operator)

Untitled Notation + Factorial

a-b-c-!-d = a-b-c---...---d---...--d---...- ... ---d--d-d starting with d lines

a-b-c-!--d = a-b-c-!-d-!-d-!-d-!-...-!-d-!-d with d -!-'s

a-b-c-!-!-d = a-b-c-!---...---d-!---...--d-!---...- ... -!---d-!--d-!-d starting with d lines

a-b-c-!!-d = a-b-c-!-!-!-...-!-!-!-d with d lines

a-b-c-!!-!!-d = a-b-c-!!-!-!-!-...-!-!-!-d with d lines

a-b-c-!!!-d = a-b-c-!!-!!-!!-...-!!-!!-!!-d with d lines

a-b-c-!!!...!!!-d = a-b-c-!!!...!!-!!!...!!-!!!...!!-...-!!!...!!-!!!...!!-d with d lines

etc.

Extended Factorial Notation

Extended Up-Arrow Notation + Factorial

a!(b)! = a!!!...!!! with b !'s

a!((b))! = a!(a!(...(a!(b)!)...)!)! with b levels

a!(!(b)!)! = a!(((...(((b))...)) with b levels

etc.

Chained Up-arrow Notation

Let a -> b = a -> a -> b in Chained Arrow Notation

Then:

a ->^ b = a -> a -> a ->...-> a -> a -> a with b ->'s

a ->^^^...^^^ b = a ->^^^...^^ a ->^^^...^^ a ->^^^...^^ a ->^^^...^^  a ... a ->^^^...^^ a ->^^^...^^ a ->^^^...^^ a with b ->^^^...^^'s

a ->-> b = a ->^^^...^^^ a with b up-arrows

etc.

Torsius Extended Factorial

Extended Factorial + Torsius Factorial

n!! = n!n

n!!m = (n!!m-1)*((n-1)!!m-1)*...*(3!!m-1)*(2!!m-1)*(1!!m-1)

n!!0 = n!!

n!!!...!!! = n!!!...!!n

n!!!...!!!m = (n!!!...!!!m-1)*((n-1)!!!...!!!m-1)*...*(3!!!...!!!m-1)*(2!!!...!!!m-1)*(1!!!...!!!m-1)

n!!!...!!!0 = n!!!...!!!

etc.

Fast-Growing Alphabet Hierarchy

Alphabet Hierarchy + Fast-Growing Hierarchy

Rules:

1. f_0(n) = n+1

2. f_a+1(n) = f_a(f_a(...(f_a(n)),,,)) with n levels

3. f_a(n) = f_a[n](n) if and only if a is a limit ordinal

4. f_$(a+1)(n) = f_#($($($(...($($($(a)))...))+1) with n levels where $ is a letter and # is the letter before it

5. f_A(0)(n) = f_w^^w(n)

6. f_A(a+1)(n) = f_A(a)^^w(n)

Extended Untitled Notation

Extended Up-Arrow Notation + Untitled Notation

a-b-c-(n)-d = a-b-c---...---d with n bars

a-b-c-((n))-d = a-b-c-(a-b-c-(a-b-c-(...(a-b-c-(a-b-c-(a-b-c-()-d)-d)-d)...)-d)-d)-d with n levels

etc.

??? (no name for this)

Aarex's Extended Up-Arrow Notation + My Extended Up-Arrow Notation

Let change a↑

  1. b into a↑(#)↑b

Then:

a↑((↑↑↑...↑↑↑))↑b = a↑(↑(↑(...(↑↑↑...↑↑↑)...)↑)↑)↑b with n levels, where there are n arrows

a↑(((↑↑↑...↑↑↑)))↑b = a↑((↑((...((↑↑↑...↑↑↑))...))↑))↑b with n levels, where there are n arrows

etc.

Other ideas

Suggest any ideas in the comments!

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.