Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a fraction between 8 and 9}

Verified step by step guidance

1. Step 1: Understand the set notation. The set is defined as {x | x is a fraction between 8 and 9}. This means we are looking at all numbers that are fractions and lie strictly between 8 and 9.
2. Step 2: Determine if the set is finite or infinite. Since there are infinitely many fractions between any two numbers, the set is infinite.
3. Step 3: Check if 10 is an element of the set. Since 10 is not between 8 and 9, it cannot be an element of the set.
4. Step 4: Conclude that the set is infinite and 10 is not an element of the set.
5. Step 5: Summarize the findings: The set is infinite, and 10 is not an element of the set.

Key Concepts

Finite vs. Infinite Sets

A finite set contains a limited number of elements, while an infinite set has no bounds and contains an endless number of elements. For example, the set of all integers is infinite, whereas the set of all students in a classroom is finite. Understanding this distinction is crucial for classifying sets correctly.

Set Notation

Set notation is a mathematical way to describe a collection of elements. The notation {x | condition} indicates a set of all x that satisfy a given condition. In the question, {x | x is a fraction between 8 and 9} describes all fractions that lie within that range, which helps in identifying the nature of the set.

Elements of a Set

An element of a set is an individual object or number that belongs to that set. To determine if a number, such as 10, is an element of a set, one must check if it meets the criteria defined by the set. In this case, since 10 is not between 8 and 9, it is not an element of the specified set.