English

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Noun

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set-builder notation

  1. (set theory) A mathematical notation for describing a set by specifying the properties that its members must satisfy.
    • 2000, Kenneth E. Hummel, Introductory Concepts for Abstract Mathematics[1], CRC Press (Chapman & Hall/CRC), page 123:
      With this idea for describing a finite set of sets, it is easy to generalize the concept to a certain infinite family   of sets  . Once again, the power of set builder notation triumphs. The sets   and   may be described more precisely with set builder notation than by enumeration.
    • 2011, Tom Bassarear, Mathematics for Elementary School Teachers, Cengage Learning, 5th Edition, page 56,
      In this case, and in many other cases, we describe the set using set-builder notation:
       
      This statement is read in English as "Q is the set of all numbers of the form   such that a and b are both integers, but b is not equal to zero."
    • 2012, Richard N. Aufmann, Joanne Lockwood, Intermediate Algebra, Cengage Learning, 8th Edition, page 6,
      A second method of representing a set is set-builder notation. Set-builder notation can be used to describe almost any set, but it is especially useful when writing infinite sets. In set-builder notation, the set of integers > −3 is written
       

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