User:Bruhify Army/Alpha's Number

Alpha's Number is the first major step of the Opti's Number. It's a bit massive though. It's just simply represented like this: $$A$$.

Counting Alpha's Number
The function of the Alpha's Number is $$a_{x}$$.

Notice: This number will have to use Square Bracket Notation.

Now we'll start counting:

$$a_{0} = 0[(0[0]0)]0 = 0[0]0 =0$$

$$a_{1} = 1[(1[1]1)]1 = 1[1+1]1 = 1[2]1 = 1 \times 1 = 1$$

$$a_{2} = 2[(2[2]2)]2 = 2[2 \times 2]2 = 2[4]2 = 2\uparrow \uparrow 2 = 4$$

$$a_{3} = 3[(3[3]3)]3 = 3[3^{3}]3 = 3[27]3$$

...And so on...

Result
The formula is $$a_{n}=n[(n[n]n)]n$$

The Alpha's Number is defined as $$a_{a_{a_{.....{_3}}}}$$, which it nested the $$a$$s for $$a_{a_{3}}$$ times.

Other Steps of Opti's Number
If this is not so big, don't forgot this is just one of the step of Opti's Number. We have more steps for the massive Opti's Number such as Beta's Number. Stay tuned for bigger numbers!