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'difference' and subtraction

  1. Mar 26, 2008 #1
    I have a dumb question. What is the difference between "difference" and "subtraction" or is the same thing. For example, 2 subtract 2 (2-2) is 0 .. But is the difference between 2 and -2 equal to 4?
     
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  3. Mar 27, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi cowah22! Welcome to PF! :smile:

    Yup … difference = subtraction!

    Except that difference is always positive (or zero).

    So you'd say "the difference between 7 and 5 is 2", and also "the difference between 5 and 7 is 2".

    So it can sometimes cause confusion.

    (And yes, the difference between 2 and -2, or between -2 and 2, is 4.)
     
  4. Mar 27, 2008 #3
    How come? sorry, still noobish, but shouldn't be -2 and 2 = -4?
     
  5. Mar 27, 2008 #4

    HallsofIvy

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    Yes, but you are comparing two different things. "2 subtract 2 (2-2) is 0" and "the difference between 2 and 2 is 0" (not -2). "2 subtract -2 (2-(-2)= 2+ 2) is 4" and "the difference between 2 and -2 is 4".

    What do you mean by "and" here? Normally "and" is interpreted as a sum: -2+ 2= 0. You seem to be thinking about -2- 2= -4.

    Here is on possible distinction between "subtraction" and "difference". The "difference between a and b" is a- b. Is the "difference between b and a" b-a or is it the same as the "difference between a and b"?

    It's really a matter of common English rather than mathematics (and so much vaguer) but typically by the "difference between two numbers" we mean the absolute value: the "difference between a and b" is |a- b|. That's what Tiny Tim said.
     
  6. Mar 27, 2008 #5

    mathwonk

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    a "difference" is the result of a "subtraction". i.e. subtraction is an operation, and a difference is an element of a group.
     
  7. Mar 27, 2008 #6
    Seems odd, that: -2 + -2 = -4 (difference is 0?)
    and the opposite: +2 - +2 = 0 (difference is 0?)

    seems strange..
     
    Last edited: Mar 27, 2008
  8. Mar 27, 2008 #7

    arildno

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    No. Here, you ADD the negative number (-2) with itself. The difference between a number and itself is, of course 0.
    Here, you SUBTRACT the positive number 2 from itself, giving 0 as the result.
     
  9. Mar 27, 2008 #8
    NOTE this is an idea that kinda makes sense and is a postulation
    that i beleive is easily proven whith the ideas Ive mentioned.
    Dont know if its actualy enough proof but its cool to think about
    Nice question by the way

    I just realized something
    very interesting

    ok draw your x-axis look
    the numbers
    2 and 4 the and number inbetween which is 3
    the difference should signifie the length of the line betwen 2 and 4 right?
    ok what about a line between 3 and 4
    4and 4

    It is the magnitude of line inbetween what ever integers you select
    subtraction is numbers and is not geomtric because you cannot have a negative length

    Therefore
    Subtraction - Non geometric
    difference - geometric
     
  10. Mar 27, 2008 #9

    tiny-tim

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    … classical v modern geometry …

    Hi Marcwhydothe! :smile:

    I get your point, but I think it depends what you mean by "geometric".

    I entirely agree that classical geometry, of the ancient Greek sort, wouldn't have been interested in negative distances.

    But modern geometry (space-time, for example) is quite used to the coordinate system in general, and vectors in particular.

    (A vector, of course, is a length and a direction.)

    So I'd be more inclined to write:

    difference - classical geometry
    subtraction - modern geometry. :smile:
     
  11. Mar 27, 2008 #10

    Strange.. My calculator told me different.
     
  12. Mar 27, 2008 #11
    Then either you mistold the calculator what you wanted it to do, or you need a new calculator.

    Think of the values on a number line. Given 0 is the origin, and you are at a value -2, which is to say two left of the origin 0. Suppose you move two further toward the left, or -2 units, you would obviously end up four units to the left, or (as any value to the left of the origin is called), -4 units.

    As for your calculator problem, on every calculator I've used there is a button that allows you to assign a negative value to a number, this is NOT the subtract button.
     
  13. Mar 28, 2008 #12
    Well, I entered: 2,+/-, +, 2, +/-, = into the calculator and it returned -4. I tried this on several calculators and the answer was -4 each time. But then I tried it on another calculator, which converted 2,+/-, +,2,+/- into:

    -(-(2)+2) which is 0 ... But if you flip this around (swap + and - signs) you get

    ((-2)-2) which is -4 Strange?
     
    Last edited: Mar 28, 2008
  14. Mar 28, 2008 #13
    How is this strange? PEMDAS. Parenthesis first, which, on your first example is -(0), which is 0.

    On your second example two to the left of 0 and two more to the left -2 is -4.
     
  15. Mar 29, 2008 #14
    How can a mathematical opposite not be the inverse, when looking at
    -2 + -2

    +2 - +2
    There shouldn't be any multiplication here, right?
     
    Last edited: Mar 29, 2008
  16. Mar 29, 2008 #15

    arildno

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    You need to lay aside crude, fallacious and vague notions like "opposite".

    You are doing two entirely different things here:

    In the first, you ADD a number to itself.

    In the second, you SUBTRACT a number from itself.
     
  17. Mar 30, 2008 #16
    Same with multiplication:
    -2 * -2 = 4 why shouldn't this be -4 ?

    2 * 2 = 4

    division: -2 / -2 = 1
    how can a positive number come from 2 negative numbers?
    2 / 2 = 1
     
  18. Mar 30, 2008 #17

    symbolipoint

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  19. Mar 30, 2008 #18

    arildno

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    Sigh. What do you mean by "come from"?

    Here, I'll show you why (-1)*(-1)=1, by reference to the axioms valid for ordinary arithmetic.

    1. (-1)+1=0 This is the basic definition of the "negative" of a number, i.e (-a)+a=0 for every number "a"

    2. Since a=b implies c*a=c*b for numbers (expressions) a,b,c, 1. implies:
    (-1)*((-1)+1)=(-1)*0

    3. Since, for all numbers a,b, c we have a*(b+c)=a*b+a*c, 2. may be rewritten as:
    (-1)*(-1)+(-1)*1=(-1)*0

    4. Now, given any number "a", we have a*1=a and a*0, thus 3. may be rewritten as:
    (-1)*(-1)+(-1)=0

    5. Now, since for any numbers/expressions a=b implies a+c=b+c, 4. implies:
    (-1)*(-1)+(-1)+1=0+1

    6. Now, invoking 1. on the left hand side, and that 0+a=a on the right hand side, we get:
    (-1)*(-1)+0=1

    7. Noting that adding 0 doesn't change the value of "a", i.e, a+0=a, we finally get:
    (-1)*(-1)=1

    which was to be proven.
     
  20. Mar 31, 2008 #19
    I just meant, if there isn't a positive number in an equation how can the result ever be negative.

    If:
    4 * 4 = 4 + 4 + 4 + 4 = 16

    Why isn't:
    -4 * -4 = -4 + -4 + -4 + -4 = -16

    I know these seem like stupid questions.. But really, where would something like -4 * -4 = 16 ever occur in nature or physics... Which math is used to explain.
     
    Last edited: Mar 31, 2008
  21. Mar 31, 2008 #20

    symbolipoint

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    Read and study the information in the link in post #17, and read the proof in post #18; and then you should clearly understand why the product of two negative numbers is a positive number.
     
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