Set Builder Notation Definition

The function must work for all values we give it so it is up to us to make sure we get the domain correct. 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.

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It is used with common types of numbers such as integers real numbers and natural numbers.

Set builder notation definition. The set x. A shorthand used to write sets often sets with an infinite number of elements. The same set could be described as x x is a counting number less than 10 in set builder notation.

For example the set 1 2 3 4 5 6 7 8 9 list the elements. Set builder notation is very useful for defining domains. In its simplest form the domain is the set of all the values that go into a function.

The symbols shown in this lesson are very appropriate in the realm of mathematics and in mathematical logic. Set builder notation is really useful for defining a domain of a function. Thus there is a variable on the left of the separator and a rule on the right of it.

This notation can also be used to express sets with an interval or an equation. For example if e x is the predicate x is an even number and if the domain of discourse for e is the set n then the notation x e x specifies the set of even natural numbers. Forming sets in this manner is also known as set comprehension set abstraction or as defining a set s intension.

Set builder notation is a shorthand used to write sets often for sets with an infinite number of elements. Set notation is used to help define the elements of a set. Set builder notation can be used to describe sets that are defined by a predicate rather than explicitly enumerated.

The domain is the set of all the values that go into a function. Uncountable set theory a mathematical notation for describing a set by stating the properties that its members must satisfy. In this form set builder notation has three parts.

A set builder notation describes or defines the elements of a set instead of listing the elements. We call this the set builder notation as you can think of the predicate as a building material for the elements of the set. X 0 is read aloud the set of all x such that x is greater than 0.

A variable a colon or vertical bar separator and a logical predicate.

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