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Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

Revision as of 13:48, 20 April 2012

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: <math>n^\text{th}\!</math> '''multiple''' of <math>x\!</math> in a group <math>\underline{X} = (X, +, 0),\!</math> for any integer <math>n,\!</math> is defined the same way for <math>n \ge 0,\!</math> letting <math>nx = (-n)(-x)\!</math> for <math>n < 0.\!</math>

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: A group <math>\underline{X} = (X, +, 0)\!</math> is '''cyclic''' if and only if there is an element <math>g \in X\!</math> such that every <math>x \in X\!</math> can be written as <math>x = ng\!</math> for some <math>n \in \mathbb{Z}.\!</math> In this case, an element such as <math>g\!</math> is called a '''generator''' of the group.

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: In a group <math>\underline{X} = (X, +, 0),\!</math> the multiple <math>nx\!</math> is defined for every integer <math>n\!</math> by letting <math>nx = (-n)(-x)\!</math> for <math>n < 0\!</math> and proceeding the same way for <math>n \ge 0.\!</math>

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: A group <math>\underline{X} = (X, +, 0)\!</math> is '''cyclic''' if and only if there is an element <math>g \in X\!</math> such that every <math>x \in X\!</math> can be written as <math>x = ng\!</math> for some <math>n \in \mathbb{Z}.\!</math> In this case, an element such as <math>g\!</math> is called a '''generator''' of the group.

Jon Awbrey

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