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Thorough explanation of sets builder Notation
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In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by stating the properties that its members must satisfy. Forming sets in this manner is also known as set comprehension, set abstraction or as defining a set's intension. Although some simply refer to it as set notation, that label may be better reserved for the broader class of means of denoting sets.
this is quite thorough http://www.mathsisfun.com/sets/set-builder-notation.html
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