Let A = { -6, - 12/4 , - 5/8 , - √3, 0, 1/4 , 1, 2π, 3, √12}. List all the elements of A that belong to each set. Integers

Verified step by step guidance

1. First, recall the definition of integers: integers are whole numbers that can be positive, negative, or zero, but they do not include fractions or irrational numbers.
2. Next, examine each element of the set \(A = \{ -6, - \frac{12}{4}, - \frac{5}{8}, - \sqrt{3}, 0, \frac{1}{4}, 1, 2\pi, 3, \sqrt{12} \}\) and determine if it is an integer.
3. Simplify any elements that are fractions or radicals to see if they reduce to integers. For example, simplify \(- \frac{12}{4}\) and \(\sqrt{12}\).
4. Check if the simplified values are whole numbers without fractional or decimal parts. If yes, include them in the list of integers.
5. Finally, list all elements from set \(A\) that meet the integer criteria based on your analysis.

Key Concepts

Set Theory and Elements

Set theory studies collections of objects called sets. Understanding how to identify and list elements within a set is fundamental. Here, the set A contains various numbers, and the task is to classify these elements based on their membership in another set, such as integers.

Integers

Integers are whole numbers that include positive numbers, negative numbers, and zero, without fractions or decimals. Recognizing integers involves checking if a number can be expressed without fractional or irrational parts, such as -6, 0, or 3.

Simplification of Numbers

Simplifying numbers like fractions and radicals helps determine their exact value and classification. For example, -12/4 simplifies to -3, and √12 simplifies to 2√3, which is irrational. Simplification is essential to correctly identify which elements are integers.