Fun With Math-Superpowerition: Inventing a Super Power Operation -- Decimal a > 1 ✱ Decimal 0 < b

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Decimal a > 1 ✱ Decimal 0 < b < 1

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

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

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

1.25 ✱ 0.00 = 1.25 ^ (1.25 ^ (0.00 - 1)) = 1.25 ^ (1.25 ^ (-1.00)) = 1.25 ^ 0.8000000 ≈ 1.1954406

1.50 ✱ 0.00 = 1.50 ^ (1.50 ^ (0.00 - 1)) = 1.50 ^ (1.50 ^ (-1.00)) ≈ 1.50 ^ 0.6666666 ≈ 1.3103706

1.75 ✱ 0.00 = 1.75 ^ (1.75 ^ (0.00 - 1)) = 1.75 ^ (1.75 ^ (-1.00)) ≈ 1.75 ^ 0.5714285 ≈ 1.3768253

2.00 ✱ 0.00 = 2.00 ^ (2.00 ^ (0.00 - 1)) = 2.00 ^ (2.00 ^ (-1.00)) = 2.00 ^ 0.5000000 ≈ 1.4142135

1.00 ✱ 0.25 = 1.00 ^ (1.00 ^ (0.25 - 1)) = 1.00 ^ (1.00 ^ (-0.75)) = 1.00 ^ 1.00 = 1.00

1.25 ✱ 0.25 = 1.25 ^ (1.25 ^ (0.25 - 1)) = 1.25 ^ (1.25 ^ (-0.75)) ≈ 1.25 ^ 0.8458970 ≈ 1.2077467

1.50 ✱ 0.25 = 1.50 ^ (1.50 ^ (0.25 - 1)) = 1.50 ^ (1.50 ^ (-0.75)) ≈ 1.50 ^ 0.7377879 ≈ 1.3487082

1.75 ✱ 0.25 = 1.75 ^ (1.75 ^ (0.25 - 1)) = 1.75 ^ (1.75 ^ (-0.75)) ≈ 1.75 ^ 0.6572361 ≈ 1.4445526

2.00 ✱ 0.25 = 2.00 ^ (2.00 ^ (0.25 - 1)) = 2.00 ^ (2.00 ^ (-0.75)) ≈ 2.00 ^ 0.5946035 ≈ 1.5100575

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

1.25 ✱ 0.50 = 1.25 ^ (1.25 ^ (0.50 - 1)) = 1.25 ^ (1.25 ^ (-0.50)) ≈ 1.25 ^ 0.8944271 ≈ 1.2208967

1.50 ✱ 0.50 = 1.50 ^ (1.50 ^ (0.50 - 1)) = 1.50 ^ (1.50 ^ (-0.50)) ≈ 1.50 ^ 0.8164965 ≈ 1.3924445

1.75 ✱ 0.50 = 1.75 ^ (1.75 ^ (0.50 - 1)) = 1.75 ^ (1.75 ^ (-0.50)) ≈ 1.75 ^ 0.7559289 ≈ 1.5265797

2.00 ✱ 0.50 = 2.00 ^ (2.00 ^ (0.50 - 1)) = 2.00 ^ (2.00 ^ (-0.50)) ≈ 2.00 ^ 0.7071067 ≈ 1.6325268

1.00 ✱ 0.75 = 1.00 ^ (1.00 ^ (0.75 - 1)) = 1.00 ^ (1.00 ^ (-0.25)) = 1.00 ^ 1.00 = 1.00

1.25 ✱ 0.75 = 1.25 ^ (1.25 ^ (0.75 - 1)) = 1.25 ^ (1.25 ^ (-0.25)) ≈ 1.25 ^ 0.9457416 ≈ 1.2349569

1.50 ✱ 0.75 = 1.50 ^ (1.50 ^ (0.75 - 1)) = 1.50 ^ (1.50 ^ (-0.25)) ≈ 1.50 ^ 0.9036020 ≈ 1.4425019

1.75 ✱ 0.75 = 1.75 ^ (1.75 ^ (0.75 - 1)) = 1.75 ^ (1.75 ^ (-0.25)) ≈ 1.75 ^ 0.8694417 ≈ 1.6266998

2.00 ✱ 0.75 = 2.00 ^ (2.00 ^ (0.75 - 1)) = 2.00 ^ (2.00 ^ (-0.25)) ≈ 2.00 ^ 0.8408964 ≈ 1.7911627

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

1.25 ✱ 1.00 = 1.25 ^ (1.25 ^ (1.00 - 1)) = 1.25 ^ (1.25 ^ ( 0.00)) = 1.25 ^ 1.00 = 1.25

1.50 ✱ 1.00 = 1.50 ^ (1.50 ^ (1.00 - 1)) = 1.50 ^ (1.50 ^ ( 0.00)) = 1.50 ^ 1.00 = 1.50

1.75 ✱ 1.00 = 1.75 ^ (1.75 ^ (1.00 - 1)) = 1.75 ^ (1.75 ^ ( 0.00)) = 1.75 ^ 1.00 = 1.75

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