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What are the subsets of rational numbers?
natural numbers integers and whole numbers
Are natural numbers subsets of positive integers?
No. Natural numbers are the same set or a superset. The answer depends on whether 0 is excluded or included in natural numbers.
What are the subsets of irrational numbers?
There are no subsets of irrational numbers. There are subsets of rational numbers, however.
What are the subsets of a real numbers?
The set of real numbers is infinitely large, therefore it has an infinite amount of subsets. For example, {1}, {.2, 4, 800}, and {-32323, 3.14159, 32/3, 6,000,000} are all subsets of the real numbers. There are a few, important, and well studied namedsubsets of the real numbers. These include, but aren't limited to, the set of all prime numbers, square numbers, positive numbers, negative numbers, natural numbers, even numbers, odd numbers, integers, rational numbers, and irrational numbers. For more information on these, and other, specific subsets of the real numbers, follow the link below.
Why are natural numbers whole numbers and integers all subsets of the set of rational numbers?
Because any natural number or whole number, n, can be expressed as a ratio of the two integers n and 1: in the form n/1. And integers are the same as whole numbers.
