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March 27, 2017

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my teacher told me that the inverse of addition was subtraction and that the inverse of subtraction was addition...

could you prove it to me

-x = (-1)x

((-1)x)^-1

I don't see how I'm suppose to get + x by taking the inverse of -x i've always been told in math to just to the opposite of subbtraction which is addition but my teacher is telling me that is a lie and that it's really the inverse of subtraction is addition but I don't see the reasoning behind it

basically can you prove to me that the opposite of subractiion is addition and vise versa??? by taking the inverses????

I don't get it...

like I can prove that the opposite of multiplication is division by taking the inverse and can prove it just by defintion

(5x = 2)5^-1 = x = 5^-1 (2)

that's how you prove that relationship is really just inverses but what about addition and subtraction how are the inverse relationships...???

Thansk

  • Very easy math - ,

    Use numbers.

    6 + 2 = 8

    Therefore, 8 - 6 = 2 or 8 - 2 = 6

    How can you state those relationships in abstract terms?

  • Very easy math - ,

    If x is some number and:

    x + y = 0

    then y is called an inverse (w.r.t. addition) of x

    Then it follows from the same definition that x is an inverse of y. Now, what you need to prove is that inverses are unique. I.e. if for some given x

    x + y = 0

    and also

    x + z = 0

    you necessarily have y = z.

    So, it then follows that the inverse of the inverse of x is x and it can't be anything else than x.

    Then, if we denote the inverse of x by
    -x, we can prove that:

    -x = (-1)*x

    THis is because:

    x + (-1)*x =

    1*x + (-1)*x =

    (1 + (-1))*x =

    0*x = 0

    Here we have used that -1 is the inverse of 1.

    So, (-1)*x satisfies the criterium the inverse of x which we always denote as
    -x must satisfy and therefore
    -x = (-1)*x

    Then the fact that taking twice the inverse yields the same number implies that:

    (-1)*(-1) = 1

  • Very easy math - ,

    i agree with all of it but still don't see how

    X + B = C
    we can simply solve for B by simply multiplying the whole equation by B^-1 which we note as -B because????

    (X + B = C)B^-1

    B cancels out

    X = B^-1 C

    what allows us to say that B^-1 is equal to -B

  • Very easy math - ,

    You are confusing terms:

    Inverse is not the reciprocal. You are using reciprocal (B^-1) is reciprocal.

    Now it is confusing, because the inverse operation to multiplication is division, and the inverse to division is multiplication
    http://www.mathsisfun.com/definitions/inverse-operation.html

    Watch the usage to "inverse", a lot of folks really mean reciprocal when they use it.

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