The Five Alephs Of Infinity -- From The Smallest To The Biggest

Here are what I understand to be the five Alephs of Infinity, from the smallest to the biggest.
These are thence the five general categories of "relative infinity," as I am able to presently perceive, from the smallest general category to the largest general category.

1)  Infinity.

2)  ((3.977746573*10^10)*Infinity)^8.

3)  ((3.977746573*10^10))^Infinity^8.

4)  (Infinity^8^Infinity^8).

5)  (e^Infinity^8^Infinity^8).

Here is part of my derivation, as to the immediately prior:

The hyperbolic tangent of 45 degrees is Infinity.  Both the sine of 45 degrees and the cosine of 45 degrees is equal to (1/(2^.5)).
sine(45 degrees)*cosine(45 degrees) =  (1/2^.5)*(1/2^.5) = 1/2.  (1/2)^5 = 1/32.
Let's say that (180 degrees/PI)/32  = x degrees.
Let's next say that (The hyperbolic tangent of (x degrees)) = y.
Let's say that y^8 = z.
Then, (33*z)^8 = ~ 3.977746573*10^10.

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.