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Math Help - builder notation for set

  1. #1
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    builder notation for set

    for this: {0,3,6,9,12}

    S={x|x \in N , x is multiply of 3, x \leq 12}

    S={x|x is multiply of 3 and 0 \leq x \leq 12}

    Which one is correct and more valid?


    and how to write for this one: {m,n,o,p} ?
    Last edited by zpwnchen; September 18th 2009 at 07:13 PM.
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  2. #2
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    Set notation

    Hello zpwnchen
    Quote Originally Posted by zpwnchen View Post
    for this: {0,3,6,9,12}

    S={x|x \in N , x is multiply of 3, x \leq 12}

    S={x|x is multiply of 3 and 0 \leq x \leq 12}

    Which one is correct and more valid?


    and how to write for this one: {m,n,o,p} ?
    First, let's be clear that the word you want here is multiple, not multiply.

    Secondly, there are two interpretations of \mathbb{N}, the natural numbers: it's either the positive integers, \{1,2,3,...\} or the non-negative integers, \{0,1,2,3,...\}. So unless you state which of these two definitions is being used, then it's best to avoid using \mathbb{N} here.

    The clearest notation to use, then, is S=\{x|x is a multiple of 3 and 0\leq x \leq 12\}.

    You could define {m, n, o, p} in a variety of ways; for example, { \lambda | \lambda is a lower-case letter and \lambda follows l and precedes q in alphabetical order}

    Grandad
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