Ch. R - Algebra Review

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. R - Algebra Review

Problem 29

Chapter 1, Problem 29

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 guidance

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.

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.

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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