Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:11 minutes

Problem 25

Textbook Question

Use set notation, and list all the elements of each set. {x | x is a natural number greater than 8 and less than 15}

Verified step by step guidance

Identify the range of natural numbers: Natural numbers are positive integers starting from 1. The problem specifies numbers greater than 8 and less than 15.

List the natural numbers within the specified range: Start from the smallest natural number greater than 8 and go up to the largest natural number less than 15.

Write down the numbers: Begin with 9, as it is the first natural number greater than 8, and end with 14, as it is the last natural number less than 15.

Express the set in set notation: Use curly braces to list the numbers identified in the previous step.

Ensure all numbers are included: Double-check that all natural numbers from 9 to 14 are listed in the set.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Notation

Set notation is a mathematical way to describe a collection of objects, known as elements. It often uses curly braces to enclose the elements or a rule to define the elements that belong to the set. For example, the notation {x | condition} indicates a set of all x that satisfy the given condition.

Natural Numbers

Natural numbers are the set of positive integers starting from 1 and extending indefinitely (1, 2, 3, ...). In this context, natural numbers are used to define the elements of the set, specifically those that are greater than 8 and less than 15. Understanding the range of natural numbers is crucial for identifying the specific elements of the set.

Inequalities

Inequalities are mathematical expressions that describe the relative size or order of two values. In this case, the inequalities 'greater than 8' and 'less than 15' define the boundaries for the natural numbers included in the set. Solving inequalities helps in determining which elements meet the specified conditions.