Set-Builder Notation
If a set’s components share a property, that property can be used to define the components. For instance, the set A = {1, 2, 3, 4, 5, 6} has a trait in common that all of its members are natural integers lower than 7. Other natural numbers do not have this characteristic. As a result, the set X may be expressed as follows:
A = {x: x is a natural number less than 7} may be translated as “A is the set of elements x such that x is a natural number less than 7.”
The set mentioned above may alternatively be expressed as A = {x: x N, x < 7}.
Another way to express set A = {the set of all natural numbers less than 7}.
In this instance, the description of a set’s common attribute is written inside brackets. This is a set-builder form or rule approach in its most basic version.
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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