FANDOM


Remake of Aarex's Game.

Rules are the same as Aarex's Version: http://googology.wikia.com/wiki/User_blog:Googleaarex/Make_an_extension_of_the_notation

New rules:

1. You can't edit previous definitions

Post your entries in the comments!

Extension 0 (original) (mine)

0#n = n+n

1#n = 0#(0#(0#(...(0#(0#(0#n)))...))) with n levels

m#n = m-1#(m-1#(m-1#(...(m-1#(m-1#(m-1#n)))...))) with n levels

Extension 1 (mine)

(0)#n = n#n

(0)0#n = (0)#n

(0)1#n = (0)1#((0)1#((0)1#(...((0)1#((0)1#((0)1#n)))...))) with n levels

(0)(0)#n = (0)n#n

(1)#n = (0)(0)(0)...(0)(0)(0)#n with n (0)'s

(1)(1)#n = (1)(0)(0)(0)...(0)(0)(0)#n with n (0)'s

(2)#n = (1)1#((1)1#((1)1#(...((1)1#((1)1#((1)1#n)))...))) with n levels

(m)#n = (m-1)m-1#((m-1)m-1#((m-1)m-1#(...((m-1)m-1#((m-1)m-1#((m-1)m-1#n)))...))) with n levels

Extension 2 (mine)

((0))#n = (n)#n

((0)0)#n = ((0))#n

((0)1)#n = ((0))((0))((0))...((0))((0))((0))#n with n ((0))'s

((0)(0))#n = ((0)n)#n

((1))#n = ((0)(0)(0)...(0)(0)(0))#n with n (0)'s

etc.

We can have ((2)), ((m)), (((0))), (((1))), ((((0)))), (((((0))))), etc.

Limit is (((...(((m)))...)))#n

Extension 3 (Sbiis)

(0,1)#n = (((...(((n)))...)))#n w/n ()s

(1,1)#n = (0,1)(0,1)...(0,1)#n w/n (0,1)s

etc.

(0,2)#n = (((...(((n,1),1),1)...,1)#n w/n ,1s

(0,(0))#n = (0,n)#n

(0,0,1)#n = (0,(0,(0,(0, ... (0,n))...))#n w/n 0,s

...

(0,0,0,1)#n = (0,0,(0,0,(0,0,(0,0,( ... (0,0,n))...))#n w/n 0,0,s

etc.

Extension 4 (mine)

(0[1]1)#n = (0,0,0,...,0,0,1)#n with n entries

(1[1]1)#n = (0[1]1)(0[1]1)(0[1]1)...(0[1]1)(0[1]1)(0[1]1)#n with n (0[1]1)'s

((0)[1]1)#n = (n[1]1)#n

(0,1[1]1)#n = ((((...(((n)))...)))[1]1)#n with n levels

etc.

Then:

(0[1]2)#n = (0,0,0,...,0,0,1[1]1)#n with n entries

(0[1](1))#n = (0[1]n)#n

(0[1]0,1)#n = (0[1](((...(((n)))...))))#n with n levels

etc.

Then:

(0[1]0[1]1)#n = (0[1]0,0,0,...,0,0,1)#n with n entries

(0[1]0[1]0[1]1)#n = (0[1]0[1]0,0,0,...,0,0,1)#n with n entries

etc.

Limit is (0[1]0[1]0[1]...0[1]0[1]0[1]1)#n

Extension 5 (Aarex)

Extension 5:

(0[2]1)#n = (0[1]0[1]0[1]...[1]0[1]0[1]1)#n with n entries

(0[2]2)#n = (0[1]0[1]0[1]...[1]0[1]0[1]1[2]1)#n with n entries

(0[2]0[2]1)#n = (0[2]0[1]0[1]0[1]...[1]0[1]0[1]1)#n with n entries

(0[3]1)#n = (0[2]0[2]0[2]...[2]0[2]0[2]1)#n with n entries

(0[m]1)#n = (0[m-1]0[m-1]0[m-1]...[m-1]0[m-1]0[m-1]1)#n with n entries

(0[(0)]1)#n = (0[n]1)#n

etc.

Limit is (0[(0[(0[...]1)]1)]1)#n

Extension 6 (Aarex)

(0[0,1]1)#n = (0[(0[(...[(0[(0[n]1)]1)]...)]1)]1)#n /w n 0's

(0[1,1]1)#n = (0[0,1]0[0,1]0[0,1]...[0,1]0[0,1]0[0,1]1)#n with n [0,1]-spaces

(0[0,2]1)#n = (0[(0[(...[(0[(0[n,1]1),1]1),1]...),1]1),1]1)#n /w n 0's

(0[0,0,1]1)#n = (0[0,(0[0,(...[0,(0[0,(0[0,n]1)]1)]...)]1)]1)#n /w n 1's

(0[0[1]1]1)#n = (0[0,0,0,...,0,0,1]1)#n /w n entries inside []

(0[0[0,1]1]1)#n = (0[0[(0[0[(...[0[(0[0[(0[0[n]1]1)]1]1)]...1])]1]1)]1)#n /w n 0's

Limit of extension 6 is (0[0[0[...]1]1]1)

Extension 7 (mine/Aarex)

Extension 7a

(0,11)#n = (0[0[0[...]1]1]1)#n with n levels

(1,11)#n = (0,11)(0,11)(0,11)...(0,11)(0,11)(0,11)#n with  (0,11)'s

etc.

(0[0,11]1,11)#n = (0[0[0[...]1]1]1,11)​#n with n levels

(0,12)#n = (0[0[0[...]1]1]1,12)#n with n levels

(0,12)#n = (0[0[0[...,11]1,11]1,11]1,11)​#n with n levels

(0,10,11)#n = (0,10[0,10[0,10[0,1...]1]1]1)​#n with n levels

(0[1]12)#n = (0,10,10,1...,10,10,11)​#n with n ,1-spaces

(0,21)#n = (0[0[0[...]11]11]11)​#n with n levels

Extension 7b

(0,0,11)#n = (0,(0,(...(0,(0,n1)1)...)1)1)​#n with n levels

etc.

(0,0,111)#n = (0,0[0,0[0,0[...]11]11]11)​#n with n levels

etc.

Limit is (0,0,0,...111)#n

Extension 8 (Aarex)

To make extension 8, let change [a]b into [a][b].

(0[0][0][1]1)#n = (0[0][0[0][0[0][...]1]1]1)#n /w n nested

(0[0][0][2]1)#n = (0[0][0[0][0[0][...][1]1][1]1][1]1)#n /w n nested

(0[0][0][0][1]1)#n = (0[0][0][0[0][0][0[0][0][...]1]1]1)#n /w n nested

Limit is (0[0][0]...[0][1]1)#n.

Extension 9 (mine)

Extension 9a

(0[0],[1]1)#n = (0[0][0]...[0][1]1)#n with n entries

(0[1],[1]1)#n = (0[0],[1]0[0],[1]0[0],[1]0...0[0],[1]0[0],[1]0[0],[1]1)#n with n [0],[1]'s

etc.

(0[0],[2]1)#n = (0[0][0]...[0][1],[1]1)#n with n entries

etc.

(0[0],[0],[1]1)#n = (0[0],[0][0]...[0][1]1)#n with n entries

etc.

Extension 9b

(0[0][ [1] ][1]1)#n = (0[0],[0],[0],...,[0],[0],[1]1)#n with n entries

(0[0][ [2] ][1]1)#n = (0[0][ [1] ][0][ [1] ][0][ [1] ]...[ [1] ][0][ [1] ][0][ [1] ][1]1)#n with n entries

etc.

(0[0][ [0] ][ [1] ][1]1)#n = (0[0][ [0[0][ [0[0][ [...[0][ [0[0][ [0[0][ [1]][1]1] ][1]1] ][1]...] ][1]1] ][1]1] ][1]1)#n with n levels

etc.

Limit is (0[0][ [0] ][ [0] ][ [0] ]...[ [0] ][ [0] ][ [1] ][1]1)#n

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