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Example of Classifying Numbers as Whole, Integer, Rational, Irrational, or Real
Given the values , rac{14}{5}, , , , and , we can systematically classify them into nested number sets:
- Whole numbers: The only whole number in the list is , since whole numbers consist of
- Integers: Includes the whole number , the negative whole opposite , and since , the negative square root .
- Rational numbers: This set includes all integers (, , ) plus all terminating or repeating fractions and decimals ( rac{14}{5} and ).
- Irrational numbers: The value is the only irrational number, because is not a perfect square, resulting in a non-repeating, non-terminating decimal.
- Real numbers: All the numbers provided are real numbers, as they fall into either the rational or irrational categories.
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Intermediate Algebra @ OpenStax
Ch.1 Foundations - Intermediate Algebra @ OpenStax
Algebra
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Example of Classifying Numbers as Whole, Integer, Rational, Irrational, or Real
A software developer is designing a data validation module that uses a nested hierarchy to classify numerical values for a corporate database. In a visual representation (Venn diagram) of this system, which set of numbers would be represented as the smallest circle contained entirely within the 'Whole Numbers' circle?