Use set-builder notation to describe each set. See Example 2. (More than one description is possible.) {4, 8, 12, 16,...}
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 31
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. Integers
Verified step by step guidance1
First, recall the definition of integers: integers are whole numbers that can be positive, negative, or zero, but they do not include fractions or irrational numbers.
Next, 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 an integer.
Simplify any elements that are fractions or radicals to see if they reduce to integers. For example, simplify \(-\frac{12}{4}\) and \(\sqrt{12}\).
Check if the simplified values are whole numbers without fractional or decimal parts. If yes, include them in the list of integers.
Finally, list all elements from \(A\) that meet the integer criteria based on your analysis.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of Integers
Integers are whole numbers that can be positive, negative, or zero, but do not include fractions or decimals. Examples include -3, 0, and 7. Understanding this helps identify which elements from a set qualify as integers.
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Introduction to Common Polar Equations
Simplification of Fractions and Radicals
To determine if elements like -12/4 or √12 are integers, simplify them first. For example, -12/4 simplifies to -3, an integer, while √12 simplifies to 2√3, which is not an integer. Simplification clarifies membership in the integer set.
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Solving Linear Equations with Fractions
Distinguishing Between Number Types
Recognizing the difference between integers, rational numbers, irrational numbers, and real numbers is crucial. For instance, 2π is irrational and not an integer, while 3 is an integer. This distinction aids in correctly classifying elements.
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Introduction to Complex Numbers
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