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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 26
Chapter 1, Problem 26

Use set notation, and list all the elements of each set. {x | x is a natural number not greater than 4}

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Understand the problem: We need to describe the set of all natural numbers that are not greater than 4 using set notation and list all the elements explicitly.
Recall that natural numbers are typically the positive integers starting from 1, so the natural numbers not greater than 4 are those numbers \( x \) such that \( x \in \mathbb{N} \) and \( x \leq 4 \).
Write the set in set-builder notation: \( \{ x \mid x \in \mathbb{N}, x \leq 4 \} \). This means the set of all natural numbers \( x \) where \( x \) is less than or equal to 4.
List all the elements of the set explicitly by identifying all natural numbers from 1 up to 4: \( \{ 1, 2, 3, 4 \} \).
Combine both parts: the set in set-builder notation and the explicit list of elements, which fully describes 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 way to describe a collection of elements using a rule or property. The notation {x | condition} means 'the set of all x such that the condition holds.' It helps define sets precisely without listing all elements explicitly.
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Natural Numbers

Natural numbers are the set of positive integers starting from 1 (sometimes including 0, depending on context). They are used for counting and ordering. Understanding which numbers qualify as natural is essential for correctly listing elements in the set.
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Inequalities and Set Restrictions

Inequalities like 'not greater than 4' restrict the elements included in a set. This means all elements must satisfy the condition x ≤ 4. Recognizing and applying such restrictions helps in accurately listing all elements of the set.
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Linear Inequalities
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