List the elements in each set. See Example 1. {z|z is an integer less than or equal to 4}

Verified step by step guidance

1. Understand the set notation: The set is defined as all integers \( z \) such that \( z \leq 4 \). This means we are looking for all integer values less than or equal to 4.
2. Recall that integers include all whole numbers, both positive and negative, including zero: \( \ldots, -3, -2, -1, 0, 1, 2, 3, 4, 5, \ldots \).
3. Since the condition is \( z \leq 4 \), the set includes 4 and all integers less than 4, extending infinitely in the negative direction.
4. To list elements explicitly, start from 4 and list integers decreasing by 1: \( 4, 3, 2, 1, 0, -1, -2, -3, \ldots \).
5. Note that because the set includes all integers less than or equal to 4, it is an infinite set extending indefinitely in the negative direction.

Key Concepts

Set Notation

Set notation is a way to describe a collection of elements that share a common property. In this question, the set is defined using a variable and a condition, such as {z | condition}, meaning all elements z that satisfy the given condition are included.

Integers

Integers are whole numbers that include positive numbers, negative numbers, and zero. Understanding that integers are discrete values without fractions or decimals is essential for listing all elements that meet the condition.

Inequalities

Inequalities express a relationship where one quantity is less than, greater than, or equal to another. Here, 'less than or equal to 4' means all integers that are 4 or smaller, which guides the selection of elements in the set.