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. Whole numbers

검증된 단계별 안내

Recall the definition of whole numbers: Whole numbers are the set of numbers that include all non-negative integers starting from 0, i.e., \(\{0, 1, 2, 3, \ldots\}\).

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 whole number.

Check if the element is a non-negative integer (0 or positive integer) without any fractional or irrational part.

Identify the elements that satisfy this condition: 0, 1, 3 (since \(\sqrt{12}\) is not an integer and \(2\pi\) is irrational, and the others are negative or fractions).

List these elements as the subset of \(A\) that are whole numbers: \(\{0, 1, 3\}\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Definition of Whole Numbers

Whole numbers are the set of non-negative integers starting from zero, including 0, 1, 2, 3, and so on. They do not include fractions, decimals, negative numbers, or irrational numbers. Understanding this helps identify which elements from a given set qualify as whole numbers.

Number Classification

Number classification involves categorizing numbers into sets such as integers, rational numbers, irrational numbers, and whole numbers. Recognizing the properties of each type allows for accurate sorting of elements based on their characteristics, such as sign, fractional form, or irrationality.

Simplification and Evaluation of Expressions

Simplifying expressions like fractions and radicals is essential to determine their exact value and type. For example, simplifying -12/4 to -3 or √12 to 2√3 helps decide if the number fits into the whole numbers set, which requires the number to be a non-negative integer.