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

-a ✱ -b

In this page, let's make both the a and b in a ✱ b negative numbers so that it becomes -a ✱ -b. We'll also let the -b be zero and a few other numbers so you can see what happens.

Let's try out some variables for a using the formula a ^ (a ^ (b - 1)). We'll let b have the values from 2 to -4 and a be the value of -1.

−1 ✱ 2 = −1 ^ (−1 ^ (2 - 1)) = −1 ^ (−1 ^ ( 1)) = −1 ^ −1 = −1
−1 ✱ 1 = −1 ^ (−1 ^ (1 - 1)) = −1 ^ (−1 ^ ( 0)) = −1 ^ 1 = −1
−1 ✱ 0 = −1 ^ (−1 ^ (0 - 1)) = −1 ^ (−1 ^ (−1)) = −1 ^ −1 = −1
−1 ✱ −1 = −1 ^ (−1 ^ (−1 - 1)) = −1 ^ (−1 ^ (−2)) = −1 ^ 1 = −1
−1 ✱ −2 = −1 ^ (−1 ^ (−2 - 1)) = −1 ^ (−1 ^ (−3)) = −1 ^ −1 = −1
−1 ✱ −3 = −1 ^ (−1 ^ (−3 - 1)) = −1 ^ (−1 ^ (−4)) = −1 ^ 1 = −1
−1 ✱ −4 = −1 ^ (−1 ^ (−4 - 1)) = −1 ^ (−1 ^ (−5)) = −1 ^ −1 = −1

As you can see, raising negative 1 to an odd power is negative 1, and raising negative 1 to an even power including zero is positive 1. As both of those values are used as expnents to raise the base of negative 1 to a power, the result is always going to be negative 1.

Therefore, −1 ✱ [any number] = −1.

−2 ✱ 2 = −2 ^ (−2 ^ (2 - 1)) = −2 ^ (−2 ^ ( 1)) = −2 ^ −2 = 1/4 (0.25)
−2 ✱ 1 = −2 ^ (−2 ^ (1 - 1)) = −2 ^ (−2 ^ ( 0)) = −2 ^ 1 = −2
−2 ✱ 0 = −2 ^ (−2 ^ (0 - 1)) = −2 ^ (−2 ^ (−1)) = −2 ^ (−1/2) = undefined
−2 ✱ −1 = −2 ^ (−2 ^ (−1 - 1)) = −2 ^ (−2 ^ (−2)) = −2 ^ (−1/4) = undefined
−2 ✱ −2 = −2 ^ (−2 ^ (−2 - 1)) = −2 ^ (−2 ^ (−3)) = −2 ^ (−1/8) = undefined
−2 ✱ −3 = −2 ^ (−2 ^ (−3 - 1)) = −2 ^ (−2 ^ (−4)) = −2 ^ (−1/16) = undefined
−2 ✱ −4 = −2 ^ (−2 ^ (−4 - 1)) = −2 ^ (−2 ^ (−5)) = −2 ^ (−1/32) = undefined
−3 ✱ 2 = −3 ^ (−3 ^ (2 - 1)) = −3 ^ (−3 ^ ( 1)) = −3 ^ −3 = −1/27 (−0.037037037037...)
−3 ✱ 1 = −3 ^ (−3 ^ (1 - 1)) = −3 ^ (−3 ^ ( 0)) = −3 ^ 1 = −3
−3 ✱ 0 = −3 ^ (−3 ^ (0 - 1)) = −3 ^ (−3 ^ (−1)) = −3 ^ (−1/3) = undefined
−3 ✱ −1 = −3 ^ (−3 ^ (−1 - 1)) = −3 ^ (−3 ^ (−2)) = −3 ^ (−1/9) = undefined
−3 ✱ −2 = −3 ^ (−3 ^ (−2 - 1)) = −3 ^ (−3 ^ (−3)) = −3 ^ (−1/27) = undefined
−3 ✱ −3 = −3 ^ (−3 ^ (−3 - 1)) = −3 ^ (−3 ^ (−4)) = −3 ^ (−1/81) = undefined
−3 ✱ −4 = −3 ^ (−3 ^ (−4 - 1)) = −3 ^ (−3 ^ (−5)) = −3 ^ (−1/243) = undefined
−4 ✱ 2 = −4 ^ (−4 ^ (2 - 1)) = −4 ^ (−4 ^ ( 1)) = −4 ^ −4 = 1/256 (0.00390625)
−4 ✱ 1 = −4 ^ (−4 ^ (1 - 1)) = −4 ^ (−4 ^ ( 0)) = −4 ^ 1 = −4
−4 ✱ 0 = −4 ^ (−4 ^ (0 - 1)) = −4 ^ (−4 ^ (−1)) = −4 ^ (−1/4) = undefined
−4 ✱ −1 = −4 ^ (−4 ^ (−1 - 1)) = −4 ^ (−4 ^ (−2)) = −4 ^ (−1/16) = undefined
−4 ✱ −2 = −4 ^ (−4 ^ (−2 - 1)) = −4 ^ (−4 ^ (−3)) = −4 ^ (−1/64) = undefined
−4 ✱ −3 = −4 ^ (−4 ^ (−3 - 1)) = −4 ^ (−4 ^ (−4)) = −4 ^ (−1/256) = undefined
−4 ✱ −4 = −4 ^ (−4 ^ (−4 - 1)) = −4 ^ (−4 ^ (−5)) = −4 ^ (−1/1024) = undefined

Well, it looks like the negative numbers for variable b has failed, except when variable a is negative 1.

Please turn to the next page for the Formula Summary So Far.

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.

Help Support Our Ad-Free Web Section

Just use our PayPal link to pay.

Please Donate Cash to help pay for webhosting, domain payments, expenses and labor in keeping this section going. Thank you.

$2, $5, $10, $20, $50, $75, $100, $ANY

Notice Of Disclosure (updated June 2023):

"David Tanny is the owner and operator of the domains davesfunstuff.com and davidtanny.com"

Website Cookie Policy