Why Do We Use Set Builder Form?
When there are many components and utilizing the roster form makes it difficult to represent the components of the set, set builder notation is employed. Let’s use an illustration to better grasp this. If you need to write a list of numbers from 1 to 8 inclusively, you may just write {1, 2, 3, 4, 5, 6, 7, 8} using the roster notation.
But when we have to list every real number, a difficulty appears. It would not be possible to use roster notation in this situation. {…, 1, 1.1, 1.01, 1.001, 1.0001, … }. However, in this case, it would be preferable to use the set-builder notation.
{x | x is a real number} OR {x | x is a rational or irrational number} is the set builder form for real numbers. Writing sets are made easier by using the set-builder notation, particularly when writing sets with an unlimited number of components. The set-builder notation may be used to express numbers like integers, real numbers, and natural numbers. Using this technique, a set containing an interval or an equation may also be represented.
Set-Builder Notation
Set-builder Notation is a type of mathematical notation used to describe sets by naming their components or highlighting the requirements that each member of the set must meet. Sets are written in the form of {y | (properties of y)} OR {y : (properties of y)} in the set-builder notation, where the condition that fully characterizes each member of the collection replaces the attributes of y.
The elements and properties are separated using the character ‘|’ or ‘:’ The entire set is interpreted as “the set of all elements y” such that (properties of y), while the symbols ‘|’ or ‘:’ are read as “such that.”
This article explores the set-builder notation, symbols used in set-builder notation, examples, representation of sets methods, etc.
Table of Content
- What is Set-Builder Notation?
- Symbols Used in Set Builder Notation
- Representation of Sets Methods
- Tabular or Roster Form
- Examples of Roster Method
- Set-Builder Notation
- Why Do We Use Set Builder Form?
- How to use a Set Builder Notation?
- How to Write a Set Builder Notation?
- How to read Set Builder Notation?
- Set Builder Notation for Domain and Range
- Set Builder Notation Examples
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