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Math Help - algebraic expressions

  1. #1
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    algebraic expressions

    I am a dad helping with daughters homework and have a symbol I have not seen, the symbol is a solid diamond. The problem reads
    A new operation is defined as a ( solid diamond ) b = a+a-b. Is the set of whole numbers closed under the operation ( solid diamond )? If not, give a set that is closed under this operation.
    Can anyone tell me what I am supposed to do with the solid diamond? Thank you in advance.
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  2. #2
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    a (diamond) b=a+a-b

    5 (diamond) 2=5+5-2=8

    The set of whole numbers is not going to be closed under this new operation (which is simply a combination of familiar operations in addition and subtraction) because the set of whole numbers is not closed under addition and subtraction

    Here I am assuming the set of whole numbers is {0,1,2,3,.....}

    however the set of integers and real numbers will be closed. The set of whole numbers are not closed because if b is large enough, a+a-b could be negative, and thus the result would not be an element of the whole numbers
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  3. #3
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    You are given  a\diamond b = a+a-b

    So now think, if a = 2 and b = 3 now

     2\diamond 3 = 2+2-3 = 1

    The diamond symbol is not an operation in particular, just defined for this particualr problem.

    Even easier

     a\diamond b = a+a-b = 2a-b
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