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 April 15th, 2012, 01:38 AM #11 Hijikata teh   Join Date: May 2004 Posts: 5,297 Re: -1 = 1 25 has two roots, one negative and one positive. Taking the root of -25 has only one result, the imaginary root (5i). Also, yes, the answer is 288. I actually made a mistake writing it down--the troll logic order is 48/2 (9+3), intentionally ambiguous to fool the reader into thinking the answer is 2 instead. (48/24 = 2) edit: Because the value of i shifts every odd exponent. Code: ```i^0 = 1 i^1 = i i^2 = -1 i^3 = -i i^4 = -1``` If you have i * i, that's not the same thing as (-1 * -1)^1/2, because exponents aren't distributive. You have to add the exponents or leave the bases separate until you resolve the exponent. __________________ I ask you, is a man not entitled to his own opinion? NO, says the forum poster. It belongs to me. Last edited by Hijikata; April 15th, 2012 at 01:45 AM.
April 15th, 2012, 01:57 AM   #12
HanzBejinker
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Re: -1 = 1

Quote:
 Originally Posted by Hijikata If you have i * i, that's not the same thing as (-1 * -1)^1/2, because exponents aren't distributive. You have to add the exponents or leave the bases separate until you resolve the exponent.
One of the properties of exponents I'm guessing. So that you can avoid situations such as this.

 April 15th, 2012, 03:22 AM #13 Hijikata teh   Join Date: May 2004 Posts: 5,297 Re: -1 = 1 I mean, look at it this way: Code: `2^2 * 2^2 = 2^4 = 16` This is a common base (2), with a common power (2). You multiply them together, and receive an increased multiplier but no change in the base. If you were to keep the exponent fixed, you would be able to multiply the bases in the above example, but you'd be wrong if you changed the numbers: Code: ```3^3 * 3^3 = 3^6 = 81 3^3 * 3^3 = (3 * 3)^3 = 729``` The proper way to handle exponent multiplication is to leave the bases the same and add the exponents. In the faulty line in the OP, you fall into the trap of the above example by keeping the exponent fixed and multiplying the bases. __________________ I ask you, is a man not entitled to his own opinion? NO, says the forum poster. It belongs to me.
 April 15th, 2012, 03:59 AM #14 Dirtbag A.K.A Gatinator     Join Date: Feb 2011 Location: Cleveland Posts: 2,131 Re: -1 = 1 If you ponder equations rather than sleep walk while laboring you will wind up a crazy janitor. They were once like us, but they chose to drive their selves mad by attempting equations. __________________ Damn! I'm so gangsta I'm too gangsta. CBS interactive... well... I'm not permitted to express what would accurately as well appropriately define CBS interactive. Those mother...
 April 15th, 2012, 11:08 AM #15 NOLAftw hi     Join Date: Aug 2010 Location: Over there Posts: 6,826 Re: -1 = 1 @Hijikata, that's incorrect. 3^6 = 729. The rule when multiplying exponential #'s is: If the bases are the same, you can add the exponents while keeping the base. If the exponents are the same, you can multiply the bases while keeping the exponent. (But you can't do both if both are the same). The reason that (-1)^1/2 * (-1)^1/2 = (-1 * -1)^1/2 is incorrect, is that in the rule Code: `√(a) * √(b) = √(a * b)` , a and/or b must be a positive, real #. __________________ Last edited by NOLAftw; April 15th, 2012 at 11:09 AM.
 April 15th, 2012, 04:18 PM #16 Hijikata teh   Join Date: May 2004 Posts: 5,297 Re: -1 = 1 That's what I get for doing math at 5 in the morning. In this topic, I am told who is the boss. __________________ I ask you, is a man not entitled to his own opinion? NO, says the forum poster. It belongs to me.
 April 15th, 2012, 07:48 PM #17 L3VIATH4N I failed the Turing test.     Join Date: Feb 2009 Location: 127.0.0.1 Posts: 5,431 Re: -1 = 1 The key here is in the definition of square root and not ignoring the fact that the square root function yields two results. The square root of a number a is y, such that y*y=a. We sort of mentally ignore one root of the square root function, but there's two. As Hiji mentioned, sqrt(25) is equal to both +5 and -5. Similarly, sqrt(-25)= +5i and -5i. -1*-1 = 1, and 1*1=1. The important distinction is that sqrt(1) =/= 1. It's a function that has two roots, +1 and -1. Similarly, 1 raised to any power isn't equal to 1. It's the component along the real axis probably has a value of 1, but there's a difference between the point 1+0i and the roots of the equation x=1^a. __________________ Do you have a question about Borderlands or the forums? Feel free to send me a private message for your questions and concerns. Remember to read the RULES and FAQs before posting. Failure to do so can result in you breaking a rule you did not know about and getting an infraction. Before creating a new topic/thread, make sure to use the search tool. Remember to avoid words three characters or less in size, as they are filtered out.
 April 16th, 2012, 08:37 PM #18 MickityMike OccurredStone     Join Date: Feb 2005 Location: St. Louis, Missouri Posts: 8,545 Re: -1 = 1 Now, let's all find the area under the curve!!11 __________________ Happily married gay couples with closets full of assault weapons. That's my vision for America, and it's a good one. -Glenn Reynolds Oh ****! - Plaxico Burress
 April 20th, 2012, 11:11 AM #19 sirmidor sophisms, know them.     Join Date: Aug 2011 Location: the land of whores, weed and tulips. Posts: 1,760 Re: -1 = 1 so it's basically the same as this: -2 =(-8)^(1/3) =(-8)^(2/6) =6√(-8)^2 =6√64=2 (just want to point out that the six before the root, doesn't mean 6 x ..., but instead root to the sixth (i have no idea how you say it in english)) __________________ there is no logical proof to support the claim that any sort of deity exists. a ''holy book'' is not proof, since it's credibility depends on the respective deity, it would be a circulus in probando to use one as argument for the other. ''religion isn't about proof, it's about belief''. you believe something BECAUSE there is proof. if a friends tells a crazy story, you might still believe him, because you've known him for a long time or something. belief requires evidence.
April 20th, 2012, 11:56 AM   #20
AkumaMishima
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Re: -1 = 1

Quote:
 Originally Posted by Hellz Lips which i suck at, which is why im a psych major.
There's more math involved in psychology academics than many, many other fields of study. Understanding and practicing statistical analysis is imperative to obtaining a workable degree in the field.
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