Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a natural number greater than 11}

Key Concepts

Finite vs. Infinite Sets

A finite set contains a limited number of elements, while an infinite set has no bounds and continues indefinitely. For example, the set of all natural numbers is infinite, as it includes 1, 2, 3, and so on without end. Understanding whether a set is finite or infinite is crucial for determining its properties and the nature of its elements.

Natural Numbers

Natural numbers are the set of positive integers starting from 1 and increasing indefinitely (1, 2, 3, ...). They are used for counting and ordering. In the context of the given set, recognizing that natural numbers do not include zero or negative numbers is essential for determining membership within the set.

Set Membership

Set membership refers to whether a specific element belongs to a particular set. In this case, to determine if 10 is an element of the set {x | x is a natural number greater than 11}, one must evaluate if 10 meets the criteria defined by the set. Since 10 is not greater than 11, it is not a member of this set.