Sure, let's define the domain for each of the given sets and for the term "all real numbers."
1. Domain of the set [tex]\(\{-2, -1, 0, 2, 5\}\)[/tex]:
- The domain of a set of numbers simply includes all the unique elements within that set.
- So, for the set [tex]\(\{-2, -1, 0, 2, 5\}\)[/tex], the domain is the set itself: [tex]\(\{-2, -1, 0, 2, 5\}\)[/tex]
- The numbers in this set are already unique and sorted in a specific order.
- Therefore, the domain of [tex]\(\{-2, -1, 0, 2, 5\}\)[/tex] is [tex]\(\{0, 2, 5, -1, -2\}\)[/tex].
2. Domain of the set [tex]\(\{3, -1, 3, 1, 2\}\)[/tex]:
- Similar to the first set, we include all unique elements of the set.
- Note that the number [tex]\(3\)[/tex] repeats, but in a set, we only consider unique values.
- So, for the set [tex]\(\{3, -1, 3, 1, 2\}\)[/tex], the unique elements are [tex]\(\{3, -1, 1, 2\}\)[/tex].
- The domain of this set, without considering the repetition and order, is [tex]\(\{1, 2, 3, -1\}\)[/tex].
3. Domain of "All Real Numbers":
- When we refer to "all real numbers," we are talking about every possible real number on the number line.
- This includes all the positive numbers, negative numbers, rational numbers (numbers that can be expressed as a fraction), and irrational numbers (numbers that cannot be expressed as a simple fraction, like [tex]\(\pi\)[/tex] or [tex]\(\sqrt{2}\)[/tex]).
- Therefore, the domain for "all real numbers" is simply stated as "all real numbers."
To conclude:
- The domain of [tex]\(\{-2, -1, 0, 2, 5\}\)[/tex] is [tex]\(\{0, 2, 5, -1, -2\}\)[/tex].
- The domain of [tex]\(\{3, -1, 3, 1, 2\}\)[/tex] is [tex]\(\{1, 2, 3, -1\}\)[/tex].
- The domain of "All Real Numbers" is "all real numbers".
