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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1:45 minutes

Problem 15

Textbook Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a natural number greater than 11}

Verified step by step guidance

Step 1: Understand the definition of the set. The set is defined as {x | x is a natural number greater than 11}. This means it includes all natural numbers starting from 12 and onwards.

Step 2: Determine if the set is finite or infinite. Since there is no upper limit to the natural numbers greater than 11, the set is infinite.

Step 3: Check if 10 is an element of the set. Since the set includes only natural numbers greater than 11, 10 is not included in the set.

Step 4: Conclude that the set is infinite and does not contain the number 10.

Step 5: Summarize the findings: The set is infinite, and 10 is not an element of the set.

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Key Concepts

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

Finite vs. Infinite Sets

A finite set contains a limited number of elements, while an infinite set has no bounds and continues indefinitely. For example, the set of all natural numbers is infinite, as it includes 1, 2, 3, and so on without end. Understanding whether a set is finite or infinite is crucial for determining its properties and the nature of its elements.

Natural Numbers

Natural numbers are the set of positive integers starting from 1 and increasing indefinitely (1, 2, 3, ...). They are used for counting and ordering. In the context of the given set, recognizing that natural numbers do not include zero or negative numbers is essential for determining membership within the set.

Set Membership

Set membership refers to whether a specific element belongs to a particular set. In this case, to determine if 10 is an element of the set {x | x is a natural number greater than 11}, one must evaluate if 10 meets the criteria defined by the set. Since 10 is not greater than 11, it is not a member of this set.