"set-builder notation" meaning in English

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          "ref": "2000, Kenneth E. Hummel, Introductory Concepts for Abstract Mathematics, CRC Press (Chapman & Hall/CRC), page 123:",
          "text": "With this idea for describing a finite set of sets, it is easy to generalize the concept to a certain infinite family #x5C;mathcal#x7B;S#x7D;#x5F;2 of sets #x5C;mathcal#x7B;S#x7D;#x5F;2#x3D;#x5C;#x7B;A#x5F;i#x5C;verti#x5C;inN#x5C;#x7D;#x3D;#x5C;#x7B;A#x5F;1,A#x5F;2,A#x5F;3,#x5C;dots,A#x5F;n,#x5C;dots#x5C;#x7D;. Once again, the power of set builder notation triumphs. The sets #x5C;mathcal#x7B;S#x7D;#x5F;1 and #x5C;mathcal#x7B;S#x7D;#x5F;2 may be described more precisely with set builder notation than by enumeration.",
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          "ref": "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",
          "text": "Q=a/b|a∈Iandb∈I,b ne 0\nThis statement is read in English as \"Q is the set of all numbers of the form a/b such that a and b are both integers, but b is not equal to zero.\""
        },
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          "text": "2012, Richard N. Aufmann, Joanne Lockwood, Intermediate Algebra, Cengage Learning, 8th Edition, page 6,\nA 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\nx|x>-3,x∈integers"
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        "A mathematical notation for describing a set by specifying the properties that its members must satisfy."
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        "(set theory) A mathematical notation for describing a set by specifying the properties that its members must satisfy."
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          "ref": "2000, Kenneth E. Hummel, Introductory Concepts for Abstract Mathematics, CRC Press (Chapman & Hall/CRC), page 123:",
          "text": "With this idea for describing a finite set of sets, it is easy to generalize the concept to a certain infinite family #x5C;mathcal#x7B;S#x7D;#x5F;2 of sets #x5C;mathcal#x7B;S#x7D;#x5F;2#x3D;#x5C;#x7B;A#x5F;i#x5C;verti#x5C;inN#x5C;#x7D;#x3D;#x5C;#x7B;A#x5F;1,A#x5F;2,A#x5F;3,#x5C;dots,A#x5F;n,#x5C;dots#x5C;#x7D;. Once again, the power of set builder notation triumphs. The sets #x5C;mathcal#x7B;S#x7D;#x5F;1 and #x5C;mathcal#x7B;S#x7D;#x5F;2 may be described more precisely with set builder notation than by enumeration.",
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          "ref": "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",
          "text": "Q=a/b|a∈Iandb∈I,b ne 0\nThis statement is read in English as \"Q is the set of all numbers of the form a/b such that a and b are both integers, but b is not equal to zero.\""
        },
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          "text": "2012, Richard N. Aufmann, Joanne Lockwood, Intermediate Algebra, Cengage Learning, 8th Edition, page 6,\nA 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\nx|x>-3,x∈integers"
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