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Why does a double negative equal a positive, but two positives don't equal a negative?

Moose 2009/04/25 19:19:51
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  • Zuggi 2009/04/25 19:26:47
    Because...
    Zuggi
    +8
    If we can agree that a negative number is just a positive number multiplied by -1, then we can always write the product of two negative numbers this way:

    (-a)(-b) = (-1)(a)(-1)(b) = (-1)(-1)ab

    For example,

    -2 * -3 = (-1)(2)(-1)(3)

    = (-1)(-1)(2)(3)

    = (-1)(-1) * 6

    So the real question is,

    (-1)(-1) = ?

    and the answer is that the following convention has been adopted:

    (-1)(-1) = +1

    This convention has been adopted for the simple reason that any other convention would cause something to break.

    For example, if we adopted the convention that (-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

    (-1)(1 + -1) = (-1)(1) + (-1)(-1)

    (-1)(0) = -1 + -1

    0 = -2

    As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."

    Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (-1)(-1) = +1.


    http://mathforum.org/dr.math/...

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Opinions

  • driley 2009/06/28 22:47:18
    Undecided
    driley
    +1
    And why can light shine through dark, but you can't cut through the light with dark.

    Inquiring minds want to know.
  • LPisLIFE 2009/05/01 20:59:46
    Because...
    LPisLIFE
    +1
    idk but math is always the place that im never curious as to WHY something does something. i love math... idk math curious love math idk math curious love math
  • DemonKiTTiE ♥ In MUSE I Tru... 2009/04/30 08:20:09
    I don't have a clue...
    DemonKiTTiE ♥ In MUSE I Trust ♥
    +1
    I had always wondered that myself.
  • Moose DemonKi... 2009/04/30 08:22:33
    Moose
    +1
    "Yeah right!"
  • DemonKi... Moose 2009/04/30 08:24:22
    DemonKiTTiE ♥ In MUSE I Trust ♥
    +1
    Naw the scary thing was that bothered me a LOT a few nights ago. have you been IN MY HEAD? If so GET OUT.... oh and tell no one what you saw in there... *blushes*
  • Moose DemonKi... 2009/04/30 08:26:40
    Moose
    +1
    Don't worry, I won't tell anybody =P but know that I was humored lol
  • DemonKi... Moose 2009/04/30 08:27:34
    DemonKiTTiE ♥ In MUSE I Trust ♥
    +1
    Well I am glad you got a glimpse into my madness. It IS pretty humoring.
  • Comrade Volizden 2009/04/26 17:31:33
    None of the above
    Comrade Volizden
    +1
    IT doesnt?

    Yeah, Right...
  • Mr. Basket 2009/04/26 12:05:42
    Because...
    Mr. Basket
    Math R dum.
  • Dan (Politicaly Incorrect) 2009/04/26 10:56:38
    None of the above
    Dan (Politicaly Incorrect)
    +2
    Yeah,Right
  • Rukasaki ~~ Hawkshadow 2009/04/25 23:35:35
    I don't have a clue...
    Rukasaki ~~ Hawkshadow
    +1
    ok im accelerated in math, but i dont get it either @_@
    and 2 wrongs dont make a right because the overly protective parents of our corrupt country said so
  • Moose Rukasak... 2009/04/25 23:39:09
    Moose
    It actually wasn't about math, but I see that's how a lot of people are taking it, see mac's answer... sorry for the confusion. http://www.sodahead.com/quest...
  • Rukasak... Moose 2009/04/25 23:40:24
    Rukasaki ~~ Hawkshadow
    +1
    oh, now i get it. it was about the wrong vs right thing... would that be why you bolded it?
  • Moose Rukasak... 2009/04/25 23:42:49
    Moose
    Yeah lol
  • scotty 2009/04/25 21:13:37
    I actually know this...
    scotty
    +2
    a positive statement corresponds to boolean true, a constant. but a negative is a function f(x) = inverse of x.
  • The Beaver 2009/04/25 20:35:45
    I don't have a clue...
    The Beaver
  • Moose The Beaver 2009/04/25 20:41:41
    Moose
    +2
    Look below this lol
  • mac -Holding Fast 2009/04/25 20:02:17
    None of the above
    mac -Holding Fast
    +1
    YEAH, RIGHT!
  • Moose mac -Ho... 2009/04/25 20:04:43
    Moose
    +1
    Wait, yeah right what? lol
  • mac -Ho... Moose 2009/04/25 20:11:53
    mac -Holding Fast
    +2
    Teacher is lecturing her class on grammatical usage. She points out that in the English language, a negative and a positive may mean a negative.

    "No, I walked." would be an example of a negative answer to the question "Did you run to school today?"

    Also, two negatives may mean a negative still.

    "No, I did not run."

    But, the teacher said to her class, two positives are never joined to mean a negative.

    To which little Johhny shouted "YEAH, RIGHT!"
  • Moose mac -Ho... 2009/04/25 20:13:24
    Moose
    +1
    It's always that rotten Johnny lol what's up with his parents?
  • mac -Ho... Moose 2009/04/25 20:14:58
    mac -Holding Fast
    +1
    Bunch of smartasses, if you ask me. :)

    bunch smartasses
  • Moose mac -Ho... 2009/04/25 20:10:14
    Moose
    +1
    Oh I see what you did there, lol double positive =)
  • mac -Ho... Moose 2009/04/25 20:13:05
  • Robynita© 2009/04/25 19:48:29
    Because...
    Robynita©
    +1
    Two negatives cancel each other out.

    Like if you say "I cannot not do that," you are really saying "I can do that" because if you can't not do something that means you can do it...
  • <--That guy 2009/04/25 19:47:56
    Because...
    <--That guy
    +1
    Zuggi pretty much said it all.
  • CitizenErased 2009/04/25 19:47:25
    Because...
    CitizenErased
    +3
    MATHS!!!

    Two wrongs might not make a right...but two rights do make a left.
  • Moose Citizen... 2009/04/25 19:49:47
    Moose
    +1
    Two rights make a left? lol Maybe I'm just really tired, but it doesn't seem like that would work lol
  • Citizen... Moose 2009/04/25 19:51:50
    CitizenErased
    +1
    Shhh...it's science!
  • Moderate - Whatever!!! Smil... 2009/04/25 19:36:16
  • Moose Moderat... 2009/04/25 19:38:20
    Moose
    +1
    That's the point ;-)
  • Moderat... Moose 2009/04/25 19:41:34
  • Seasoned BN-0 2009/04/25 19:34:19
    I don't have a clue...
    Seasoned BN-0
    +1
    Lets see what happens (O:
    clue
  • Moose Seasone... 2009/04/25 19:37:37
  • BoJay 2009/04/25 19:28:45
    Because...
    BoJay
    +1
    One is positive and one is negitive. positive negitive
  • AdventPhantom .::New Holoca... 2009/04/25 19:26:52
  • Zuggi 2009/04/25 19:26:47
    Because...
    Zuggi
    +8
    If we can agree that a negative number is just a positive number multiplied by -1, then we can always write the product of two negative numbers this way:

    (-a)(-b) = (-1)(a)(-1)(b) = (-1)(-1)ab

    For example,

    -2 * -3 = (-1)(2)(-1)(3)

    = (-1)(-1)(2)(3)

    = (-1)(-1) * 6

    So the real question is,

    (-1)(-1) = ?

    and the answer is that the following convention has been adopted:

    (-1)(-1) = +1

    This convention has been adopted for the simple reason that any other convention would cause something to break.

    For example, if we adopted the convention that (-1)(-1) = -1, the distributive property of multiplication wouldn't work for negative numbers:

    (-1)(1 + -1) = (-1)(1) + (-1)(-1)

    (-1)(0) = -1 + -1

    0 = -2

    As Sherlock Holmes observed, "When you have excluded the impossible, whatever remains, however improbable, must be the truth."

    Since everything except +1 can be excluded as impossible, it follows that, however improbable it seems, (-1)(-1) = +1.


    http://mathforum.org/dr.math/...
  • AdventP... Zuggi 2009/04/25 19:27:56
  • Moose Zuggi 2009/04/25 19:28:18
    Moose
    +2
    Damn Zuggi lol, You have one for literary usage as well?
  • Zuggi Moose 2009/04/25 19:29:43

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