Match the Real Number subset to the set of numbers given. Each subset will be used.
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{1, 2, 3, 4, 5...}
The set of numbers {1, 2, 3, 4, 5...} corresponds to the subset of Natural Numbers.
The set of numbers {1, 2, 3, 4, 5...} belongs to the subset of Natural Numbers.
To match the given set of numbers {1, 2, 3, 4, 5...} to the corresponding real number subsets, we can analyze the nature of the given set.
The set {1, 2, 3, 4, 5...} represents the set of natural numbers (also known as counting numbers) because it starts at 1 and continues indefinitely in ascending order without any gaps.
Now, let's match this set to the relevant subsets of real numbers:
1. Natural numbers (N): This subset consists of all positive whole numbers, including zero. Since the given set contains only positive whole numbers starting from 1, it is a subset of natural numbers (N).
2. Whole numbers (W): This subset includes all positive and negative whole numbers, including zero. Since the given set does not include negative numbers, it is not a subset of whole numbers (W).
3. Integers (Z): This subset includes all positive and negative whole numbers, including zero. Since the given set does not contain negative numbers, it is not a subset of integers (Z).
4. Rational numbers (Q): Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. The given set consists of whole numbers, which can also be expressed as fractions with a denominator of 1. Therefore, every number in the given set can be expressed as a ratio of two integers, and it is a subset of rational numbers (Q).
5. Irrational numbers (I): Irrational numbers are numbers that cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal representations. Since the given set only consists of whole numbers, it does not contain any irrational numbers. Therefore, it is not a subset of irrational numbers (I).
6. Real numbers (R): Real numbers include both rational and irrational numbers. Since the given set is a subset of rational numbers (Q), it is also a subset of real numbers (R).
To summarize, the matching real number subsets for the given set {1, 2, 3, 4, 5...} are:
- Natural numbers (N)
- Rational numbers (Q)
- Real numbers (R)