Rational Numbers Set Builder Notation

Set builder notation is a shorthand used to write sets often for sets with an infinite number of elements.

Rational numbers set builder notation. Set builder notation is a notation for describing a set by indicating the properties that its members must satisfy. Begin aligned mathbb n mbox the set of natural numbers mathbb z mbox the set of integers mathbb q mbox the set of rational numbers mathbb r mbox the set of real numbers. End aligned all these are infinite sets because they all contain infinitely many elements. We designate these notations for some special sets of numbers.

2 u 3 we used a u to mean union the joining together of two sets. Set builder notation looks like this. Set of integers an alternate notation to represent a set is the set builder notation. The domain is the set of all the values that go into a function.

Using interval notation it looks like. Jenn founder calcworkshop 15 years experience licensed certified. In set theory and its applications to logic mathematics and computer science set builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy. For a function f x 2 x 1 f x 2 x 1 the domain would be all real numbers except 1.

For example the set of natural numbers between and is represented by. P q z q 0 set of irrational numbers q x x is not rational. Set builder notation is really useful for defining a domain of a function. Set builder notation for rational and irrational number set of rational numbers or quotient of integers q x x.

We use a variable such as or to denote an element of the set and describe what properties that variable must satisfy for it to stand for elements in the set.