User blog:Nayuta Ito/Command Notation

First, I have to say a sad thing... This number is very salad.

notation
This notation is lower compatible of arrow and chain notation.

First, I use 4 signs: $$\leftarrow,\rightarrow,\uparrow,\downarrow$$.

And see this table:

Definitions of words
command is a sequence of arrows.

$$\uparrow$$ and $$\downarrow$$ are arrowy.

$$\leftarrow$$ and $$\rightarrow$$ are chainy.

Definitions of notations
In and below this section, capital letters are command and small letters are numbers.

Commands are defined from right to left.

If the last one is arrowy
If the command is made with one arrow,

$$a\uparrow b=a^b$$

$$a\downarrow b=a\uparrow^{b}a$$

Otherwise,

$$aC\uparrow b=aCaC...(btimes a's)...Ca$$

$$aC\downarrow b=aCaC...(btimes a's)...Ca$$

If the last one is chainy
If the last one is same as the one before last:

$$aC\rightarrow b C\rightarrow c=aC\rightarrow (aC\rightarrow (b-1) C\rightarrow c) C\rightarrow c-1$$

(note: this rule is same if the last is $$\leftarrow$$ .) 

(note2: If any 1's is in this notation, after that,, including the one,, is deleted.)

Otherwise:

$$aC\rightarrow b=aC\uparrow b$$

$$aC\leftarrow b=a\rightarrow^{b}a$$

This is hard to understand, so I will give you an example.

$$3\leftarrow\leftarrow3$$

$$=3\leftarrow\uparrow3$$

$$=3\leftarrow3\leftarrow3$$

$$=3\leftarrow(3\leftarrow2\leftarrow3)\leftarrow2$$

$$=3\leftarrow(3\leftarrow(3\leftarrow1\leftarrow3)\leftarrow2)\leftarrow2$$

$$=3\leftarrow(3\leftarrow3\leftarrow2)\leftarrow2$$

$$=...$$

Just writing notaions is not fun. Last but not least, I will write a number:

Unreasonable number = $$3\rightarrow\downarrow\uparrow\rightarrow\rightarrow\downarrow\rightarrow\rightarrow\uparrow\uparrow\downarrow\downarrow\leftarrow\rightarrow\leftarrow\rightarrow3$$