Set-builder notation

English

Noun

1. Template:Lb A mathematical notation for describing a set by specifying the properties that its members must satisfy.
   • Template:Quote-book
   • 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:

     $Q=\{\frac{a}{b}|a\in I\mathrm{a}\mathrm{n}\mathrm{d}b\in I,b\ne 0\}$

     This statement is read in English as "Q is the set of all numbers of the form $\frac{a}{b}$ 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

     $\{x|x>-3,x\in \mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{g}\mathrm{e}\mathrm{r}\mathrm{s}\}$

Further reading

• Template:Pedia
• Template:Pedia
• "Set-Builder Notation" in Mathwords.