User blog:Nayuta Ito/My arrow notation, which supposed to be Γ 0

ERROR: THIS IS A MESS.

It is an extension of chained arrow notation.

First Extension
$$ X_1,X_2 $$ is an array and $$Y$$ is an array of (0 or more) 1's.

a,b,c are integers more than 1 (excluding 1).

If the multiple rules can be applied, the earlier one is more prior.

$$[a][X_1]=a$$

$$[a,b][1]=a\rightarrow b$$

$$[a,b][Y,c,X_2]=[a,a,\cdots a][b,b,\cdots b,c-1,X_2]$$ ,where there are b a's and as many b's as the length of Y.

$$[X_1,1][X_2]=[X_1][X_2]$$

$$[X_1,1,a][X_2]=[X_1][X_2]$$

$$[X_1,a,b][X_2]=[X_1,([X_1,x-1,b][X_2]),b-1][X_2]$$

Googolosism: Rame Number=$$[8,2,55,33][444,8,33,2,7777,999]$$

Second Extension
$$ X_1,X_2 $$ is an array, $$Y_1$$ is an array of 1 or more 1's, $$Y_2$$ is an array of 0 or more 1's, $$Z$$and $$Z_2$$ are separators.

If the multiple rules can be applied, the earlier one is more prior.

$$[a][X_1]=a$$

$$[a,b][1]=a\rightarrow b$$

$$[a,b][XZ1]=[a,b][X]$$

$$[a,b][cZX]=[a,a,\cdots a][c-1ZX]$$,where there are b a's and as many b's as the length of Y_2.

$$[a,b][Y_2,cZX]=[a,b][b,b,\cdots b,c-1ZX]$$ ,where there are b a's and as many b's as the length of Y_2.

$$[a,b][Y_1ZY_2cZ_2X_2]=[a,b][Y_1Zb,b,\cdots b,c-1Z_2X_2]$$ ,where there are b b's.

$$[a,b][Y_1ZcZ_2X_2]=[a,b][Y_1`Z`b`Z`b\cdots `Z`b`Z`c-1Z_2X_2]$$ ,where there are b b's.

$$[X_1,1][X_2]=[X_1][X_2]$$

$$[X_1,1,a][X_2]=[X_1][X_2]$$

$$[X_1,a,b][X_2]=[X_1,([X_1,x-1,b][X_2]),b-1][X_2]$$

$$`[n]`=[n-1]$$

$$`[nZX]`=[n-1ZX]$$

$$`[Y_2,cZX]`=[b,b\cdots bc-1ZX]$$ ,where there are as many b's as the length of Y_2, and b is the value from the original array.

$$`[Y_1ZcZ_2X]`=[Y_1`Z`b`Z`b\cdots `Z`b`Z`c-1Z_2X]$$ ,where there are as many b's as the length of Y_2, and b is the value from the original array.

Googologism: Numeric Spell "Epsilon Zero" =$$[3,3][1,2[3[4[5]4]3]2,1]$$