Solved on Dec 09, 2023
Determine if the set is finite or infinite.
STEP 1
Assumptions
1. The set in question is .
2. The definition of a finite set is one that has a countable number of elements.
3. The definition of an infinite set is one that has an uncountable or endless number of elements.
STEP 2
Understand the definition of the set given. The set contains all real numbers that are larger than 18.
STEP 3
Recognize that real numbers include not just whole numbers, but also fractions, decimals, and irrational numbers.
STEP 4
Acknowledge that between any two real numbers, there are infinitely many other real numbers. For example, between 18 and 19, there are numbers like 18.1, 18.01, 18.001, and so on, ad infinitum.
STEP 5
Conclude that since there are infinitely many real numbers greater than 18, the set contains an infinite number of elements.
STEP 6
Choose the correct answer based on the conclusion that the set is infinite.
The correct answer is:
D. The set is infinite because the elements of the set are not listed between the braces, separated by commas.
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