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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

1 ✱ a

We've been looking at the Superpowerition operations involving integers of "2" and above

In this page, we'll look at the integer of "1" by placing it to the left of the superpowerition notation symbol:

1 ✱ b

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

1 ✱ 2 = 1 ^ 1 = 1 ^ (1 ^ (2 - 1)) = 1 ^ (1 ^ 1) = 1 ^ 1 = 1

1 ✱ 3 = 1 ^ 1 ^ 1 = 1 ^ (1 ^ (3 - 1)) = 1 ^ (1 ^ 2) = 1 ^ 1 = 1

1 ✱ 6 = 1 ^ 1 ^ ... ^ 1 = 1 ^ (1 ^ (6 - 1)) = 1 ^ (1 ^ 5) = 1 ^ 1 = 1

1 ✱ 10 = 1 ^ 1 ^ ... ^ 1 = 1 ^ (1 ^ (10 - 1)) = 1 ^ (1 ^ 9) = 1 ^ 1 = 1

1 ✱ 1,000 = 1 ^ 1 ^ ... ^ 1 = 1 ^ (1 ^ (1,000 - 1)) = 1 ^ (1 ^ 999) = 1 ^ 1 = 1

Well, it looks like no matter what value we put into variable b, the answer is always going to be 1 in the expression 1 ✱ b.

Therefore, 1 ✱ [any number] = 1.

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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
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