Math and Arithmetic
Numbers
Irrational Numbers

# The rational numbers are a subset of the irrational numbers?

###### Answered 2011-12-11 22:44:05

No, they are complementary sets. No rational number is irrational and no irrational number is rational.

Irrational means not rational.

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## Related Questions

Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.

Irrational Numbers, Rational Numbers, Integers, Whole numbers, Natural numbers

No, integers are a subset of rational numbers.

They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.They can be rational, irrational or complex numbers.

Starting at the top, we have the real numbers. The rational numbers is a subset of the reals. So are the irrational numbers. Now some rationals are integers so that is a subset of the rationals. Then a subset of the integers is the whole numbers. The natural numbers is a subset of those.

Natural numbers are a part of rational numbers. All the natural numbers can be categorized in rational numbers like 1, 2,3 are also rational numbers.Irrational numbers are those numbers which are not rational and can be repeated as 0.3333333.

yes * * * * * No. Rational and irrational numbers are two DISJOINT subsets of the real numbers. That is, no rational number is irrational and no irrational is rational.

For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.

Real numbers are defined as the set of rational numbers together with irrational numbers. So rationals are a subset of reals, by definition.

There are infiitelt many subsets of irrational numbers. One possible subset is the set of all positive irrational numbers.

The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.

Yes. In mathematics there are irrational numbers that are a subset of real numbers. In real life, there are actions taken that are irrational but the fact that they are taken makes them part of reality.

It is a non-integer. It can be a rational fraction (in decimal or rational form); it can be an irrational number (including transcendental numbers); it could be a complex number or a quaternion.

No, rational numbers are not a subset of integers.

Some would say that there is no intersection. However, if the set of irrational numbers is considered as a group then closure requires rationals to be a proper subset of the irrationals.

No. But all whole numbers are in the set of rational numbers. Natural numbers (&#8469;) are a subset of Integers (&#8484;), which are a subset of Rational numbers (&#8474;), which are a subset of Real numbers (&#8477;),which is a subset of the Complex numbers (&#8450;).

Integers are a subset of rational numbers which are a subset of real numbers which are a subset of complex numbers ...

Irrational numbers are never rational numbers

No. Real numbers are divided into two DISJOINT (non-overlapping) sets: rational numbers and irrational numbers. A rational number cannot be irrational, and an irrational number cannot be rational.

All rational and irrational numbers are real numbers.

Both irrational and rational are real. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.

No, they are disjoint sets: no rational is irrational and no irrational is rational.

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