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Math

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I just need a description of the following:
Associative property of Multiplication
Associative Property of Addition
Commutative properties
Distributive Property
Identity property(I don't need to know much about this)
Zero property(i don't need to know much about this)

  • Math - ,

    ADDITION:
    associative a+(b+c) = (a+b) + c
    commutative a+b = b+a
    identity : there is a number 0 with
    a+0=0+a = a
    inverse a + -a = -a + a = 0

    MULTIPLICATION:
    associative a(bc) = (ab)c
    commutative ab=ba
    identity there is a number 1 with
    a*1 = 1*a = a
    inverse If a not zero then there is an 1/a such that a(1/a) = (1/a)a = 1

    BOTH (the biggie!!)
    distributive a(b+c) = ab + ac

  • Math - ,

    thank u soooooooooooooooo much, i really needed to understand this.

  • Math - ,

    Associative property of Multiplication:

    (x*y)*z = x*(y*z)

    Associative property of Addition:

    (x + y) + z = x + (y + z)

    Commutative properties:

    x*y = y*x

    x + y = y + x

    Distributive Property :

    x*(y + z) = x*y + x*z

    Identity property: There exists a number 1 such that:

    1*x = x for all x.

    Zero property: There exists a number 0 such that:

    0 + x = x for all x

    Inverse properties:

    For every x there exists a number -x, such that:

    x + (-x) = 0

    For every x not equal to zero there exists a number x^(-1), such that:

    x*x^(-1) = 1


    Examples:

    There can only be one 0. Proof suppose there were two numbers 0 and 0' that both satisfy the property that the zero element has to satsify, then:

    0 + 0' = 0'

    because 0 is a zero element.

    But because 0' is also a zero element, you also have:

    0 + 0' = 0

    This means that 0 = 0'


    Example:

    (-1)*x = -x

    Proof:

    Let's check of (-1)*x satisfies the criterium of being the inverse (relative to addition) of x:

    x + (-1)*x =

    1*x + (-1)*x =

    (1 + (-1))*x = (use that -1 is the inverse relative to addition of 1)

    0*x = 0

    So, we can conclude that (-1)*x is the inverse of x relative to addition, which means that (-1)*x = -x

  • Math - ,

    thank u soooooo much!

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