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

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Decimal a > 1 ✱ Decimal b < 0

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

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

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

1.25 ✱ -1.00 = 1.25 ^ (1.25 ^ (-1.00 - 1)) = 1.25 ^ (1.25 ^ (-2.00)) = 1.25 ^ 0.6400000 ≈ 1.1535127

1.50 ✱ -1.00 = 1.50 ^ (1.50 ^ (-1.00 - 1)) = 1.50 ^ (1.50 ^ (-2.00)) ≈ 1.50 ^ 0.4444444 ≈ 1.1974648

1.75 ✱ -1.00 = 1.75 ^ (1.75 ^ (-1.00 - 1)) = 1.75 ^ (1.75 ^ (-2.00)) ≈ 1.75 ^ 0.3265306 ≈ 1.2004922

2.00 ✱ -1.00 = 2.00 ^ (2.00 ^ (-1.00 - 1)) = 2.00 ^ (2.00 ^ (-2.00)) = 2.00 ^ 0.25 ≈ 1.1892071

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

1.25 ✱ -0.75 = 1.25 ^ (1.25 ^ (-0.75 - 1)) = 1.25 ^ (1.25 ^ (-1.75)) ≈ 1.25 ^ 0.6767176 ≈ 1.1630026

1.50 ✱ -0.75 = 1.50 ^ (1.50 ^ (-0.75 - 1)) = 1.50 ^ (1.50 ^ (-1.75)) ≈ 1.50 ^ 0.4918586 ≈ 1.2207085

1.75 ✱ -0.75 = 1.75 ^ (1.75 ^ (-0.75 - 1)) = 1.75 ^ (1.75 ^ (-1.75)) ≈ 1.75 ^ 0.3755635 ≈ 1.2338893

2.00 ✱ -0.75 = 2.00 ^ (2.00 ^ (-0.75 - 1)) = 2.00 ^ (2.00 ^ (-1.75)) ≈ 2.00 ^ 0.2973017 ≈ 1.2288439

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

1.25 ✱ -0.50 = 1.25 ^ (1.25 ^ (-0.50 - 1)) = 1.25 ^ (1.25 ^ (-1.50)) ≈ 1.25 ^ 0.7155417 ≈ 1.1731219

1.50 ✱ -0.50 = 1.50 ^ (1.50 ^ (-0.50 - 1)) = 1.50 ^ (1.50 ^ (-1.50)) ≈ 1.50 ^ 0.5443310 ≈ 1.2469583

1.75 ✱ -0.50 = 1.75 ^ (1.75 ^ (-0.50 - 1)) = 1.75 ^ (1.75 ^ (-1.50)) ≈ 1.75 ^ 0.4319593 ≈ 1.2734518

2.00 ✱ -0.50 = 2.00 ^ (2.00 ^ (-0.50 - 1)) = 2.00 ^ (2.00 ^ (-1.50)) ≈ 2.00 ^ 0.3535533 ≈ 1.2777036

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

1.25 ✱ -0.25 = 1.25 ^ (1.25 ^ (-0.25 - 1)) = 1.25 ^ (1.25 ^ (-1.25)) ≈ 1.25 ^ 0.7565932 ≈ 1.1839175

1.50 ✱ -0.25 = 1.50 ^ (1.50 ^ (-0.25 - 1)) = 1.50 ^ (1.50 ^ (-1.25)) ≈ 1.50 ^ 0.6024013 ≈ 1.2766669

1.75 ✱ -0.25 = 1.75 ^ (1.75 ^ (-0.25 - 1)) = 1.75 ^ (1.75 ^ (-1.25)) ≈ 1.75 ^ 0.4968238 ≈ 1.3205263

2.00 ✱ -0.25 = 2.00 ^ (2.00 ^ (-0.25 - 1)) = 2.00 ^ (2.00 ^ (-1.25)) ≈ 2.00 ^ 0.4204482 ≈ 1.3383432

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