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Maybe stupid question - zero positive or negative ?

  1. Dec 3, 2008 #1

    JPC

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    1. The problem statement, all variables and given/known data

    Hi
    I have to say true or false, and then demonstrate my answer
    "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign"

    For me its true, i was thinking of creating a triplet (x, y, z), where
    x=1 if "a" positive, x=0 if "a" negative, same for y, and z
    and show that with the all the (x, y, z) possibilities, you had always 2 of the same sign

    But then, i realized, what if one of the reals a, b, c is equal to 0 ?
    like if (a, b, c) = (0, 0, 0)

    Is zero considered positive or negative, or both ?

    If so, i would have to add another value to the reals of the (x, y, z) triplet , 2, which i can then take as positive when i need or as negative when i need
     
  2. jcsd
  3. Dec 3, 2008 #2

    Mark44

    Staff: Mentor

    Zero is neither positiive nor negative.
    Any real number that is positive is greater than zero, and any negative real number is less than zero.
     
  4. Dec 3, 2008 #3

    JPC

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    ok thank you
    then i must reply false to the proposition "if taking any 3 Real numbers (a, b, c), we have at least 2 of the same sign", because with (0, 0, 0) for example , we have none of the same sign
     
  5. Dec 3, 2008 #4

    Mark44

    Staff: Mentor

    Right. Another example is (1, 0, -1).
     
  6. Dec 3, 2008 #5

    JPC

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    ok, thank you, you helped me save time not doing a long and incorrect maths demonstration :)
     
  7. Dec 4, 2008 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No. 0 is neither positive nor negative but is "its own sign". A better example is (-1, 0, 1).
     
    Last edited: Dec 4, 2008
  8. Dec 4, 2008 #7
    0 is non-negative.
     
  9. Dec 5, 2008 #8

    HallsofIvy

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    Which does not answer the question (which had already been answered). 0 is also non-positive.
     
  10. Dec 9, 2008 #9
    As others have already said, 0 is neither. 0 is basically the line between positive and negative.
    :)
     
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