Fun With Math-Superpowerition: Inventing a Super Power Operation -- Decimal 0 < a

You are at the section Fun With Math-Superpowerition: Inventing a Super Power Operation

Decimal 0 < a < 1 ✱ Decimal b > 1

Now let's let a be a decimal number between 0 and 1 and b be a decimal value between 1 and 2 using steps of 0.25.

Let's try out some variables for a using the formula a ^ (a ^ (b - 1)).

0.00 ✱ 1.00 = 0.00 ^ (0.00 ^ (1.00 - 1)) = 0.00 ^ (0.00 ^ (0.00)) = 0.00 ^ undefined = undefined

0.25 ✱ 1.00 = 0.25 ^ (0.25 ^ (1.00 - 1)) = 0.25 ^ (0.25 ^ (0.00)) = 0.25 ^ 1.00 = 0.25

0.50 ✱ 1.00 = 0.50 ^ (0.50 ^ (1.00 - 1)) = 0.50 ^ (0.50 ^ (0.00)) = 0.50 ^ 1.00 = 0.50

0.75 ✱ 1.00 = 0.75 ^ (0.75 ^ (1.00 - 1)) = 0.75 ^ (0.75 ^ (0.00)) = 0.75 ^ 1.00 = 0.75

1.00 ✱ 1.00 = 1.00 ^ (1.00 ^ (1.00 - 1)) = 1.00 ^ (1.00 ^ (0.00)) = 1.00 ^ 1.00 = 1.00

0.00 ✱ 1.25 = 0.00 ^ (0.00 ^ (1.25 - 1)) = 0.00 ^ (0.00 ^ (0.25)) = 0.00 ^ 0.00 = undefined

0.25 ✱ 1.25 = 0.25 ^ (0.25 ^ (1.25 - 1)) = 0.25 ^ (0.25 ^ (0.25)) ≈ 0.25 ^ 0.7071067 ≈ 0.3752142

0.50 ✱ 1.25 = 0.50 ^ (0.50 ^ (1.25 - 1)) = 0.50 ^ (0.50 ^ (0.25)) ≈ 0.50 ^ 0.8408964 ≈ 0.5582965

0.75 ✱ 1.25 = 0.75 ^ (0.75 ^ (1.25 - 1)) = 0.75 ^ (0.75 ^ (0.25)) ≈ 0.75 ^ 0.9306048 ≈ 0.7651232

1.00 ✱ 1.25 = 1.00 ^ (1.00 ^ (1.25 - 1)) = 1.00 ^ (1.00 ^ (0.25)) = 1.00 ^ 1.00 = 1.00

0.00 ✱ 1.50 = 0.00 ^ (0.00 ^ (1.50 - 1)) = 0.00 ^ (0.00 ^ (0.50)) = 0.00 ^ 0.00 = undefined

0.25 ✱ 1.50 = 0.25 ^ (0.25 ^ (1.50 - 1)) = 0.25 ^ (0.25 ^ (0.50)) = 0.25 ^ 0.50 = 0.50

0.50 ✱ 1.50 = 0.50 ^ (0.50 ^ (1.50 - 1)) = 0.50 ^ (0.50 ^ (0.50)) ≈ 0.50 ^ 0.7071067 ≈ 0.6125473

0.75 ✱ 1.50 = 0.75 ^ (0.75 ^ (1.50 - 1)) = 0.75 ^ (0.75 ^ (0.50)) ≈ 0.75 ^ 0.8660254 ≈ 0.7794708

1.00 ✱ 1.50 = 1.00 ^ (1.00 ^ (1.50 - 1)) = 1.00 ^ (1.00 ^ (0.50)) = 1.00 ^ 1.00 = 1.00

0.00 ✱ 1.75 = 0.00 ^ (0.00 ^ (1.75 - 1)) = 0.00 ^ (0.00 ^ (0.75)) = 0.00 ^ 0.00 = undefined

0.25 ✱ 1.75 = 0.25 ^ (0.25 ^ (1.75 - 1)) = 0.25 ^ (0.25 ^ (0.75)) ≈ 0.25 ^ 0.3535533 ≈ 0.6125474

0.50 ✱ 1.75 = 0.50 ^ (0.50 ^ (1.75 - 1)) = 0.50 ^ (0.50 ^ (0.75)) ≈ 0.50 ^ 0.5946035 ≈ 0.6622264

0.75 ✱ 1.75 = 0.75 ^ (0.75 ^ (1.75 - 1)) = 0.75 ^ (0.75 ^ (0.75)) ≈ 0.75 ^ 0.8059274 ≈ 0.7930643

1.00 ✱ 1.75 = 1.00 ^ (1.00 ^ (1.75 - 1)) = 1.00 ^ (1.00 ^ (0.75)) = 1.00 ^ 1.00 = 1.00

0.00 ✱ 2.00 = 0.00 ^ (0.00 ^ (2.00 - 1)) = 0.00 ^ (0.00 ^ (1.00)) = 0.00 ^ 0.00 = undefined

0.25 ✱ 2.00 = 0.25 ^ (0.25 ^ (2.00 - 1)) = 0.25 ^ (0.25 ^ (1.00)) = 0.25 ^ 0.25 ≈ 0.7071067

0.50 ✱ 2.00 = 0.50 ^ (0.50 ^ (2.00 - 1)) = 0.50 ^ (0.50 ^ (1.00)) = 0.50 ^ 0.50 ≈ 0.7071067

0.75 ✱ 2.00 = 0.75 ^ (0.75 ^ (2.00 - 1)) = 0.75 ^ (0.75 ^ (1.00)) = 0.75 ^ 0.75 ≈ 0.8059274

1.00 ✱ 2.00 = 1.00 ^ (1.00 ^ (2.00 - 1)) = 1.00 ^ (1.00 ^ (1.00)) = 1.00 ^ 1.00 = 1.00