Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {4, 5, 6,...., 15}

Verified step by step guidance

1. First, observe the notation of the set: {4, 5, 6, ..., 15}. The ellipsis (...) indicates a sequence of numbers starting at 4 and continuing up to 15.
2. Since the set lists numbers from 4 to 15 without skipping any integers, it contains all integers 4, 5, 6, ..., 15 inclusive.
3. Count the number of elements: from 4 to 15, there are \$15 - 4 + 1 = 12$ elements, which is a finite number.
4. Therefore, the set is a finite set because it contains a limited number of elements.
5. To check if 10 is an element of the set, see if 10 lies between 4 and 15 inclusive. Since \(4 \leq 10 \leq 15\), 10 is indeed an element of the set.

Key Concepts

Finite and Infinite Sets

A finite set contains a countable number of elements, meaning you can list all members explicitly. An infinite set has endless elements and cannot be fully listed. Understanding whether a set is finite or infinite helps classify its size and properties.

Set Notation and Elements

Set notation uses curly braces {} to list elements or describe a pattern. Elements are the individual members inside the set. Recognizing how elements are presented helps determine membership and the nature of the set.

Membership in a Set

Determining if a number is an element of a set involves checking if it fits the set's defined criteria or is explicitly listed. For example, to see if 10 is in {4, 5, 6, ..., 15}, verify if 10 lies within the range or pattern described.