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Math Help - Simple question

  1. #1
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    Simple question

    Generators of \mathbb{Z} are <1> \ \text{and} \ <-1> correct?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

    Quote Originally Posted by dwsmith View Post
    Generators of \mathbb{Z} are <1> \ \text{and} \ <-1> correct?
    No! Generators of \mathbb{Z} are 1 and -1.
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  3. #3
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    Re: Simple question

    Quote Originally Posted by alexmahone View Post
    No! Generators of \mathbb{Z} are 1 and -1.
    No? I just listed 1 and -1 too.
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  4. #4
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

    Quote Originally Posted by dwsmith View Post
    No? I just listed 1 and -1 too.
    You listed <1> \ \text{and} \ <-1>.
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  5. #5
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    Re: Simple question

    Quote Originally Posted by alexmahone View Post
    You listed <1> \ \text{and} \ <-1>.

    Generating set of a group - Wikipedia, the free encyclopedia
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

    <n> denotes the subgroup generated by n.

    So, <1>=<-1>=\mathbb{Z}

    It doesn't make sense to say that the generators of \mathbb{Z} are \mathbb{Z} and \mathbb{Z}, which is what you essentially did.
    Last edited by alexmahone; October 3rd 2011 at 03:29 PM.
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  7. #7
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    Re: Simple question

    Quote Originally Posted by alexmahone View Post
    <1> is the subgroup generated by 1, which is Z^{+}. Similarly, <-1> is the subgroup generated by -1, which is Z^{-}.

    It doesn't make sense to say that the generators of \mathbb{Z} are Z^{+} and Z^{-}, which is what you essentially did.

    "The integers under addition are an example of an infinite group which is finitely generated by both <1> and <−1>"

    Paragraph 1 after the contents
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  8. #8
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

    Quote Originally Posted by dwsmith View Post
    "The integers under addition are an example of an infinite group which is finitely generated by both <1> and <−1>"

    Paragraph 1 after the contents
    Not any more. (I've fixed that error now.)

    In general, Wikipedia is not a good place to learn maths from.
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  9. #9
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

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  10. #10
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    Re: Simple question

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  11. #11
    MHF Contributor alexmahone's Avatar
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    Re: Simple question

    Quote Originally Posted by dwsmith View Post
    Number 23 says that <-1>=<1>=\mathbb{Z}, which is what I said in post #6.
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