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Math Help - Find a special set

  1. #1
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    Find a special set

    Give a natural example of nonempty sets X \subseteq Y with a common binary operation * where both X and Y have identity elements, but they are not the same.

    Umm... I can't really think of anything, every set of integer mod would have 1 as identity...
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  2. #2
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    Quote Originally Posted by tttcomrader View Post
    Give a natural example of nonempty sets X \subseteq Y with a common binary operation * where both X and Y have identity elements, but they are not the same.

    Umm... I can't really think of anything, every set of integer mod would have 1 as identity...
    Let Y = \mathbb{Z} under multiplication. Note 1 is the identity element for Y.
    Let X = \{ 0\} under multiplication. Note 0 is the identity element for X.
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