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

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Decimal a > 1 ✱ Decimal b > 1

Now let's let a be a decimal number between 1 and 2 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)).

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

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

1.25 ✱ 1.25 = 1.25 ^ (1.25 ^ (1.25 - 1)) = 1.25 ^ (1.25 ^ (0.25)) ≈ 1.25 ^ 1.0573712 ≈ 1.2661053

1.50 ✱ 1.25 = 1.50 ^ (1.50 ^ (1.25 - 1)) = 1.50 ^ (1.50 ^ (0.25)) ≈ 1.50 ^ 1.1066819 ≈ 1.5663074

1.75 ✱ 1.25 = 1.75 ^ (1.75 ^ (1.25 - 1)) = 1.75 ^ (1.75 ^ (0.25)) ≈ 1.75 ^ 1.1501633 ≈ 1.9034148

2.00 ✱ 1.25 = 2.00 ^ (2.00 ^ (1.25 - 1)) = 2.00 ^ (2.00 ^ (0.25)) ≈ 2.00 ^ 1.1892071 ≈ 2.2802738

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

1.25 ✱ 1.50 = 1.25 ^ (1.25 ^ (1.50 - 1)) = 1.25 ^ (1.25 ^ (0.50)) ≈ 1.25 ^ 1.1180339 ≈ 1.2833605

1.50 ✱ 1.50 = 1.50 ^ (1.50 ^ (1.50 - 1)) = 1.50 ^ (1.50 ^ (0.50)) ≈ 1.50 ^ 1.2247448 ≈ 1.6431108

1.75 ✱ 1.50 = 1.75 ^ (1.75 ^ (1.50 - 1)) = 1.75 ^ (1.75 ^ (0.50)) ≈ 1.75 ^ 1.3228756 ≈ 2.0965687

2.00 ✱ 1.50 = 2.00 ^ (2.00 ^ (1.50 - 1)) = 2.00 ^ (2.00 ^ (0.50)) ≈ 2.00 ^ 1.4142135 ≈ 2.6651440

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

1.25 ✱ 1.75 = 1.25 ^ (1.25 ^ (1.75 - 1)) = 1.25 ^ (1.25 ^ (0.75)) ≈ 1.25 ^ 1.1821770 ≈ 1.3018615

1.50 ✱ 1.75 = 1.50 ^ (1.50 ^ (1.75 - 1)) = 1.50 ^ (1.50 ^ (0.75)) ≈ 1.50 ^ 1.3554030 ≈ 1.7325054

1.75 ✱ 1.75 = 1.75 ^ (1.75 ^ (1.75 - 1)) = 1.75 ^ (1.75 ^ (0.75)) ≈ 1.75 ^ 1.5215230 ≈ 2.3430846

2.00 ✱ 1.75 = 2.00 ^ (2.00 ^ (1.75 - 1)) = 2.00 ^ (2.00 ^ (0.75)) ≈ 2.00 ^ 1.6817928 ≈ 3.2082638

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

1.25 ✱ 2.00 = 1.25 ^ (1.25 ^ (2.00 - 1)) = 1.25 ^ (1.25 ^ (1.00)) = 1.25 ^ 1.25 ≈ 1.3217140

1.50 ✱ 2.00 = 1.50 ^ (1.50 ^ (2.00 - 1)) = 1.50 ^ (1.50 ^ (1.00)) = 1.50 ^ 1.50 ≈ 1.8371173

1.75 ✱ 2.00 = 1.75 ^ (1.75 ^ (2.00 - 1)) = 1.75 ^ (1.75 ^ (1.00)) = 1.75 ^ 1.75 ≈ 2.6626653

2.00 ✱ 2.00 = 2.00 ^ (2.00 ^ (2.00 - 1)) = 2.00 ^ (2.00 ^ (1.00)) = 2.00 ^ 2.00 = 4.00