List the elements in each set. See Example 1. {x|x is a whole number less than 6}

Verified step by step guidance

1. Understand the problem: We need to list all elements \( x \) such that \( x \) is a whole number less than 6.
2. Recall the definition of whole numbers: Whole numbers are non-negative integers starting from 0, i.e., \( 0, 1, 2, 3, \ldots \).
3. Identify the whole numbers less than 6: These are all whole numbers \( x \) where \( x < 6 \).
4. List the elements: Write down all whole numbers starting from 0 up to the largest whole number less than 6.
5. Express the set explicitly: The set \( \{ x \mid x \text{ is a whole number less than } 6 \} \) is \( \{ 0, 1, 2, 3, 4, 5 \} \).

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 by a condition on its elements, using curly braces and a vertical bar to mean 'such that'. Understanding this helps identify which numbers belong to the set.

Whole Numbers

Whole numbers are the set of non-negative integers starting from zero (0, 1, 2, 3, ...). Recognizing that the elements must be whole numbers restricts the possible values to these integers, excluding fractions, decimals, and negative numbers.

Inequalities and Their Interpretation

Inequalities express a range of values that satisfy a condition. Here, 'less than 6' means all whole numbers strictly smaller than 6, so elements must be less than 6 but can include zero and positive integers up to 5. Understanding inequalities helps list all valid elements.