List the elements of each set. For example, the elements of...

List the elements of each set. For example, the elements of $\{x \mid x$ is a natural number less than 4$\}$ can be listed as \{1,2,3\} . (Objective 1)
$\{x \mid x$ is a whole number less than 0$\}$

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Key Concepts

Set Builder Notation

Set builder notation is a way of specifying a set by stating a condition that its elements must satisfy. Instead of listing all members explicitly, a property or rule is provided that defines the set, making it especially useful for infinite sets or when the pattern of the elements is more important than individual values.

Whole Numbers

Whole numbers are the non-negative integers, which typically include 0 along with the counting numbers (0, 1, 2, 3, ...). This concept distinguishes whole numbers from other number sets that include negatives or fractions, setting a clear boundary on what values are considered within this group.

Empty Set

An empty set is a set that contains no elements. It occurs when the conditions specified for membership do not hold true for any element within the domain being considered. Recognizing an empty set is important when a defined condition logically excludes all potential candidates that might otherwise be expected to be part of the set.

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