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There is a show on our cable network called "the challenge" on which the following question was asked of high school students.

Is the set {-1, 0, 1} closed under: 1) addition 2) multiplication 3) both 4) neither

The student's answer was "both" but the moderator said the "correct" answer was "addition". I may be missing something obvious but wasn't the student correct?

  • 9
    Neither the student nor the moderator gave the correct answer.2012-01-26
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    If these are integers with standard addition and multiplication, then this set is **only** closed under multiplication. Note that $1+1=2$ is not in the set.2012-01-26
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    This set is only closed under multiplication.2012-01-26
  • 0
    Was the moderator a mathematician? If not, can he honestly claim to be qualified for the job?2012-01-26

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