Home DFS SB OD SDN

Notice: How To Tip The Webmaster.

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

Click to Select a Page... Main Page Introduction Comparing The Math Operators I Comparing The Math Operators II Using Numbers 3 and Higher 1 ✱ b a ✱ 1 a ✱ 0 0 ✱ b a ✱ -b -a ✱ b -a ✱ -b Formula Summary So Far Integer a > 1 ✱ Decimal b > 1 Integer a > 1 ✱ Decimal 0 < b < 1 Integer a > 1 ✱ Decimal b < 0 Decimal a > 1 ✱ Decimal b > 1 Decimal a > 1 ✱ Decimal 0 < b < 1 Decimal a > 1 ✱ Decimal b < 0 Decimal 0 < a < 1 ✱ Decimal b > 1 Decimal 0 < a < 1 ✱ Decimal 0 < b < 1 Decimal 0 < a < 1 ✱ Decimal b < 0 Decimal -2 < a < 0 ✱ Decimal -1 < b < 2 Formula Summary So Far II Why 2 ✱ 0 is Not 1 Finding The Inverse Operations 1.25 ✱ -10 to 10 1.5 ✱ -10 to 10 1.75 ✱ -10 to 10 2 ✱ -10 to 10 2.5 ✱ -10 to 10 3 ✱ -10 to 10 3.5 ✱ -10 to 10 4 ✱ -10 to 10 4.5 ✱ -10 to 10 5 ✱ -10 to 10 6 ✱ -10 to 10 7 ✱ -10 to 10 8 ✱ -10 to 10 9 ✱ -10 to 10 10 ✱ -10 to 10 Fun With Math Strip Home Page DavesFunStuff Dave's Fun Stuff Find your favorite TV shows with "Let's Watch TV!" Dave's Fun Stuff SDN Media News and More Dave's Fun Stuff Super Birthdays Contact Webmaster

Integer a > 1 ✱ Decimal b < 0

On this page, let's make the a in "a ✱ b" an integer > 1 and the b < 0.

Let's try out some variables for a using the formula a ^ (a ^ (b - 1)). Let's let b go from -1 to 0 in 0.25 steps.

Let's let a = 2.

2 ✱ -1.00 = 2 ^ (2 ^ (-1.00 - 1)) = 2 ^ (2 ^ (-2.00)) = 2 ^ 0.2500000 ≈ 1.1892071

2 ✱ -0.75 = 2 ^ (2 ^ (-0.75 - 1)) = 2 ^ (2 ^ (-1.75)) ≈ 2 ^ 0.2973017 ≈ 1.2288439

2 ✱ -0.50 = 2 ^ (2 ^ (-0.50 - 1)) = 2 ^ (2 ^ (-1.50)) ≈ 2 ^ 0.3535533 ≈ 1.2777036

2 ✱ -0.25 = 2 ^ (2 ^ (-0.25 - 1)) = 2 ^ (2 ^ (-1.25)) ≈ 2 ^ 0.4204482 ≈ 1.3383432

2 ✱ 0.00 = 2 ^ (2 ^ ( 0.00 - 1)) = 2 ^ (2 ^ (-1.00)) = 2 ^ 0.5000000 ≈ 1.4142135

2 ✱ -1.00 is the fourth root of 2 and 2 ✱ 0.00 is the square root of 2.

Let's let a = 4.

4 ✱ -1.00 = 4 ^ (4 ^ (-1.00 - 1)) = 4 ^ (4 ^ (-2.00)) = 4 ^ 0.0625000 ≈ 1.0905077

4 ✱ -0.75 = 4 ^ (4 ^ (-0.75 - 1)) = 4 ^ (4 ^ (-1.75)) ≈ 4 ^ 0.0883883 ≈ 1.1303555

4 ✱ -0.50 = 4 ^ (4 ^ (-0.50 - 1)) = 4 ^ (4 ^ (-1.50)) ≈ 4 ^ 0.1250000 ≈ 1.1892071

4 ✱ -0.25 = 4 ^ (4 ^ (-0.25 - 1)) = 4 ^ (4 ^ (-1.25)) ≈ 4 ^ 0.1767766 ≈ 1.2777035

4 ✱ 0.00 = 4 ^ (4 ^ ( 0.00 - 1)) = 4 ^ (4 ^ (-1.00)) = 4 ^ 0.2500000 ≈ 1.4142135

4 ✱ 0.00 = 2 ✱ 0.00 and 4 ✱ -0.50 = 2 ✱ -1.00.

Let's let a = 2 and b go from -2 to 0 in 0.25 steps.

2 ✱ -2.00 = 2 ^ (2 ^ (-2.00 - 1)) = 2 ^ (2 ^ (-3.00)) = 2 ^ 0.1250000 ≈ 1.0905077

2 ✱ -1.75 = 2 ^ (2 ^ (-1.75 - 1)) = 2 ^ (2 ^ (-2.75)) ≈ 2 ^ 0.1486508 ≈ 1.1085378

2 ✱ -1.50 = 2 ^ (2 ^ (-1.50 - 1)) = 2 ^ (2 ^ (-2.50)) ≈ 2 ^ 0.1767766 ≈ 1.1303555

2 ✱ -1.25 = 2 ^ (2 ^ (-1.25 - 1)) = 2 ^ (2 ^ (-2.25)) ≈ 2 ^ 0.2102241 ≈ 1.1568678

2 ✱ -1.00 = 2 ^ (2 ^ (-1.00 - 1)) = 2 ^ (2 ^ (-2.00)) = 2 ^ 0.2500000 ≈ 1.1892071

2 ✱ -0.75 = 2 ^ (2 ^ (-0.75 - 1)) = 2 ^ (2 ^ (-1.75)) ≈ 2 ^ 0.2973017 ≈ 1.2288439

2 ✱ -0.50 = 2 ^ (2 ^ (-0.50 - 1)) = 2 ^ (2 ^ (-1.50)) ≈ 2 ^ 0.3535533 ≈ 1.2777036

2 ✱ -0.25 = 2 ^ (2 ^ (-0.25 - 1)) = 2 ^ (2 ^ (-1.25)) ≈ 2 ^ 0.4204482 ≈ 1.3383432

2 ✱ 0.00 = 2 ^ (2 ^ ( 0.00 - 1)) = 2 ^ (2 ^ (-1.00)) = 2 ^ 0.5000000 ≈ 1.4142135

As the value of b gets smaller and smaller, the answer gets closer and closer to 1, but only a negative infinity for the value of b would make the answer be 1.

Menu:
Fun With Math-Superpowerition: Inventing a Super Power Operation Main Page Introduction Comparing The Math Operators I Comparing The Math Operators II Using Numbers 3 and Higher 1 ✱ b a ✱ 1 a ✱ 0 0 ✱ b a ✱ -b -a ✱ b -a ✱ -b Formula Summary So Far Integer a > 1 ✱ Decimal b > 1 Integer a > 1 ✱ Decimal 0 < b < 1 Integer a > 1 ✱ Decimal b < 0 Decimal a > 1 ✱ Decimal b > 1 Decimal a > 1 ✱ Decimal 0 < b < 1 Decimal a > 1 ✱ Decimal b < 0 Decimal 0 < a < 1 ✱ Decimal b > 1 Decimal 0 < a < 1 ✱ Decimal 0 < b < 1 Decimal 0 < a < 1 ✱ Decimal b < 0 Decimal -2 < a < 0 ✱ Decimal -1 < b < 2 Formula Summary So Far II Why 2 ✱ 0 is Not 1 Finding The Inverse Operations 1.25 ✱ -10 to 10 1.5 ✱ -10 to 10 1.75 ✱ -10 to 10 2 ✱ -10 to 10 2.5 ✱ -10 to 10 3 ✱ -10 to 10 3.5 ✱ -10 to 10 4 ✱ -10 to 10 4.5 ✱ -10 to 10 5 ✱ -10 to 10 6 ✱ -10 to 10 7 ✱ -10 to 10 8 ✱ -10 to 10 9 ✱ -10 to 10 10 ✱ -10 to 10
Related:
Fun With Math Strip Home Page DavesFunStuff
Market Zone:
Dave's Fun Stuff
TV Zone:
Find your favorite TV shows with "Let's Watch TV!"
Notable:
Dave's Fun Stuff SDN Media News and More
Footer:
Dave's Fun Stuff Super Birthdays Contact Webmaster



© 1995-2023. davesfunstuff.com. All Rights Reserved. Reproduction of any part of this website without expressed written consent is prohibited.