List the elements in each set. See Example 1. {x|x is an irrational number that is also rational}
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Functions
Problem 29
Textbook Question
Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. See Example 3. Natural numbers
Verified step by step guidance1
Recall the definition of natural numbers: they are the set of positive integers starting from 1, i.e., \(\{1, 2, 3, 4, \ldots\}\).
Examine each element of the set \(A = \{-6, -\frac{12}{4}, -\frac{5}{8}, -\sqrt{3}, 0, \frac{1}{4}, 1, 2\pi, 3, \sqrt{12}\}\) to determine if it is a natural number.
Check if the element is a positive integer without any fractional or irrational part. For example, \$1\( and \)3$ are positive integers, so they are natural numbers.
Exclude any negative numbers, zero, fractions, irrational numbers, or multiples of \(\pi\) since these do not belong to the natural numbers.
List all elements from \(A\) that satisfy the natural number criteria based on the above checks.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of Natural Numbers
Natural numbers are the set of positive integers starting from 1, typically used for counting (1, 2, 3, ...). They do not include zero, negative numbers, fractions, or irrational numbers. Understanding this helps identify which elements from a given set qualify as natural numbers.
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Classification of Numbers
Numbers can be classified into various sets such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Recognizing these categories allows one to correctly sort elements based on their properties, such as sign, fractional form, or irrationality.
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Simplification and Evaluation of Expressions
To determine if elements belong to a certain number set, expressions like fractions or roots must be simplified or approximated. For example, simplifying -12/4 to -3 or √12 to 2√3 helps in accurately classifying the numbers within the set.
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