List the elements in each set. See Example 1. {z|z is a natural number greater than 4}

Verified step by step guidance

1. Understand the problem: We need to list all elements of the set defined by the condition \(z\) is a natural number greater than 4.
2. Recall the definition of natural numbers: Natural numbers are the set of positive integers starting from 1, i.e., \(\{1, 2, 3, 4, 5, \ldots\}\).
3. Apply the condition 'greater than 4' to the natural numbers: This means we consider all natural numbers \(z\) such that \(z > 4\).
4. Write the elements of the set starting from the smallest natural number greater than 4, which is 5, and continue listing the numbers in increasing order: \(\{5, 6, 7, 8, \ldots\}\).
5. Since the set includes all natural numbers greater than 4 without an upper bound, the set is infinite and can be expressed as \(\{z \in \mathbb{N} \mid z > 4\} = \{5, 6, 7, 8, \ldots\}\).

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 condition inside braces, indicating all elements z that satisfy the given property.

Natural Numbers

Natural numbers are the set of positive integers starting from 1 (1, 2, 3, ...). Understanding this helps identify which numbers qualify as elements of the set, especially when conditions like 'greater than 4' are applied.

Inequalities in Set Definitions

Inequalities specify the range of values included in a set. Here, 'greater than 4' means all natural numbers strictly larger than 4 are included, so elements start from 5 onwards.