Difference between revisions of "Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6"
Jon Awbrey (talk | contribs) (Created page with '==Discussion== ==Work Area== ===Alternate Text=== A '''semigroup''' consists of a nonempty set with an associative LOC on it. On formal occasions, a semigroup is introduced b…') |
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| − | A '''semigroup''' consists of a nonempty set with an associative LOC on it. On formal occasions, a semigroup is introduced by means a formula like <math> | + | A '''semigroup''' consists of a nonempty set with an associative LOC on it. On formal occasions, a semigroup is introduced by means a formula like <math>X = (X, *),\!</math> interpreted to mean that a semigroup <math>X\!</math> is specified by giving two pieces of data, a nonempty set that conventionally, if somewhat ambiguously, goes under the same name <math>{}^{\backprime\backprime} X {}^{\prime\prime},\!</math> plus an associative binary operation denoted by <math>{}^{\backprime\backprime} * {}^{\prime\prime}.\!</math> In contexts where there is only one semigroup being discussed, or where the additional structure is otherwise understood, it is common practice to call the semigroup by the name of the underlying set. In contexts where more than one semigroup is formed on the same set, one may use notations like <math>X_i = (X, *_i)\!</math> to distinguish them. |
Revision as of 17:54, 19 April 2012
Discussion
Work Area
Alternate Text
A semigroup consists of a nonempty set with an associative LOC on it. On formal occasions, a semigroup is introduced by means a formula like \(X = (X, *),\!\) interpreted to mean that a semigroup \(X\!\) is specified by giving two pieces of data, a nonempty set that conventionally, if somewhat ambiguously, goes under the same name \({}^{\backprime\backprime} X {}^{\prime\prime},\!\) plus an associative binary operation denoted by \({}^{\backprime\backprime} * {}^{\prime\prime}.\!\) In contexts where there is only one semigroup being discussed, or where the additional structure is otherwise understood, it is common practice to call the semigroup by the name of the underlying set. In contexts where more than one semigroup is formed on the same set, one may use notations like \(X_i = (X, *_i)\!\) to distinguish them.
