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Q: What is the union of the sets of rational and irrational numbers?

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The real numbers.

The rational numbers are a subset of the real numbers. You might recall that rational numbers are those that can be expressed as the ratio of two whole numbers (no matter how large they are). Irrational numbers, like pi, cannot. But both sets (the rational and irrational numbers) are subsets of the real numbers. In fact, when we look at all the numbers, we are looking at the complex number system. We break that down into the real and the imaginary numbers. And the real numbers have the rational and irrational numbers as subsets. It's just that simple.

By definition, the two sets do not overlap. This is because the irrationals are defined as the set of real numbers that are not members of the rationals.

Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.Continuity is a characteristic of functions not of sets.The set of rational number is infinitely dense. This means that between any two rational numbers, no matter how close together, there are infinitely many rational numbers. And then, between any two of them these is an infinte number of rational numbers, and so on.But, in case that gives you any wrong ideas, between any two rational numbers there is an even higher order of infinity of irrational numbers. In that respect the number of gaps in the set of rational numbers (where the irrational numbers would be) is greater than the cardinality of rational numbers.

integers and rational numbers

Related questions

The real numbers.

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

No, they are complementary sets. No rational number is irrational and no irrational number is rational.Irrational means not rational.

No. The intersection of the two sets is null. Irrational numbers are defined as real numbers that are NOT rational.

Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than 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.

No, they are disjoint sets.

Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.

there are 5 diffeerent sets Natural Numbers whole numbers integers rational numbers irrational numbers.

No. Although there are infinitely many of either, there are more irrational numbers than rational numbers. The cardinality of the set of rational numbers is Ã€0 (Aleph-null) while the cardinality of the set of irrational numbers is 2Ã€0.

The sets of natural numbers, even numbers, odd numbers, prime numbers, rational numbers, irrational numbers, algebraic numbers, trascendental numbers, complex numbers, the sets of points in an euclidean space, etc.The sets of natural numbers, even numbers, odd numbers, prime numbers, rational numbers, irrational numbers, algebraic numbers, trascendental numbers, complex numbers, the sets of points in an euclidean space, etc.The sets of natural numbers, even numbers, odd numbers, prime numbers, rational numbers, irrational numbers, algebraic numbers, trascendental numbers, complex numbers, the sets of points in an euclidean space, etc.The sets of natural numbers, even numbers, odd numbers, prime numbers, rational numbers, irrational numbers, algebraic numbers, trascendental numbers, complex numbers, the sets of points in an euclidean space, etc.

No, it is uncountable. The set of real numbers is uncountable and the set of rational numbers is countable, since the set of real numbers is simply the union of both, it follows that the set of irrational numbers must also be uncountable. (The union of two countable sets is countable.)

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