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Math Help - Finite set of integers closed under addition

  1. #1
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    Finite set of integers closed under addition

    Can any finite set of integers be closed under addition? Prove your answer.

    I kind of have an understanding of what this means but don't know how to prove this?
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Can any finite set of integers be closed under addition? Prove your answer.

    I kind of have an understanding of what this means but don't know how to prove this?
    {0}
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  3. #3
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    Hello, acevipa!

    Can any finite set of integers be closed under addition? Prove your answer.

    Suppose the set is: . S \:=\:\{a,\:b,\:c,\:\hdots\:n\} . . . in increasing order.

    . . \text{If }n\text{ is positive: }\:n+n\;\notin S

    . . \text{If }a\text{ is negative: }\:a+a\;\notin S

    The set is not closed under addition.


    The only such set is a trivial one: . \{0\}


    Edit: too slow . . . again !
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