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There are infinitely many subsets of real numbers. For example, {2}, {2, 3}, {2.3, pi, sqrt(37)}. It is, therefore, not possible to list them.

The main subsets of real numbers are the rational numbers and Irrational Numbers.

Irrational numbers can be split into transcendental numbers and polynomial roots.

Rational numbers contain the set of integers.

Integers contain the set of natural numbers.

Natural numbers contain the set of counting numbers.

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There are infinitely many possible subsets.For example,

{}, {1}, {2}, {1, 2}, {3}, {1,3}, {2, 3}, {1,2,3} and so on. With n elements, you will have 2^n subsets. There are infinitely many positive integers, an equal number of negative integers, rational numbers, and a higher order of infinitely many irrational numbers in the set of Real numbers. So enumerating or even classifying the subsets is an infinitely huge task!

Q: What are the subsets of real numbers?

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The two main DISJOINT subsets of the Real numbers are the rational numbers and the irrational numbers.

Rational Numbers and Irrational Numbers

Rational numbers.

There are no subsets of irrational numbers. There are subsets of rational numbers, however.

Are disjoint and complementary subsets of the set of real numbers.

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The two main DISJOINT subsets of the Real numbers are the rational numbers and the irrational numbers.

There are infinitely many subsets of real numbers. For example, {2, sqrt(27), -9.37} is one subset.

Both are subsets of the real numbers.

Rational Numbers and Irrational Numbers

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Rational numbers.

rational numbers and irrational numbers

Only a set can have subsets, a number such as -2.38 cannot have subsets.

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.

There are no subsets of irrational numbers. There are subsets of rational numbers, however.

Both rational numbers and integers are subsets of the set of real numbers.

No, but the majority of real numbers are irrational. The set of real numbers is made up from the disjoint subsets of rational numbers and irrational numbers.

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