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set builder notation

 

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Set Builder Notation - Amazon Search

Definition:

Set builder notation is a mathematical notation used to describe a set by specifying the properties or characteristics that its elements must possess. It is commonly used in set theory and algebra.

Examples:

As a Noun (Mathematics):

  1. The prime numbers can be defined using set builder notation as {x | x is a positive integer and x is only divisible by 1 and itself}.
  2. The set of all even numbers can be represented in set builder notation as {x | x is an integer and x is divisible by 2}.

As a Noun (Programming):

  1. In programming, set builder notation is commonly used to create dynamic sets based on specific conditions. For instance, you can use set builder notation to create a set of all positive integers less than 10 in Python: {x for x in range(10) if x > 0}.
  2. Set builder notation is also useful in database queries where you may want to retrieve a set of records that meet certain criteria. For example, SELECT * FROM customers WHERE age <= 30 AND city = 'New York'.

As a Noun (Education):

  1. In education, set builder notation is often taught to students to represent solutions to inequalities or to express specific subsets. For example, the solution set for x > 5 can be written in set builder notation as {x | x is a real number and x is greater than 5}.
  2. When solving equations with multiple variables, set builder notation allows us to express constraints elegantly. For instance, the solution set for x + y = 10 can be denoted as { (x, y) | x is a real number, y is a real number, and x + y = 10 }.

As a Noun (General):

  1. Set builder notation is a valuable tool for defining sets in various fields, including mathematics, computer science, and education.
  2. Understanding set builder notation enables us to precisely describe sets based on their defining characteristics or conditions.
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