Use set notation, and list all the elements of each set. {x | x is a natural number not greater than 4}

Verified step by step guidance

1. Understand the problem: We need to list all natural numbers that are not greater than 4.
2. Recall that natural numbers are positive integers starting from 1.
3. Identify the natural numbers that are less than or equal to 4: These are 1, 2, 3, and 4.
4. Write the set using set notation: {1, 2, 3, 4}.
5. Verify that all elements listed are natural numbers and satisfy the condition of being not greater than 4.

Key Concepts

Set Notation

Set notation is a mathematical way to describe a collection of objects, known as elements. It often uses curly braces to enclose the elements or a rule to define the elements that belong to the set. For example, the notation {x | condition} indicates the set of all x that satisfy the given condition.

Natural Numbers

Natural numbers are the set of positive integers starting from 1 and extending indefinitely (1, 2, 3, ...). In some contexts, they may also include 0. Understanding natural numbers is crucial for identifying the elements of the set in the given question, as it specifies the type of numbers to consider.

Inequalities

Inequalities are mathematical expressions that describe the relative size or order of two values. In this case, the phrase 'not greater than 4' indicates an upper limit for the natural numbers in the set. This helps in determining which natural numbers are included in the set, specifically those that are 1, 2, 3, and 4.