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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.

Q: Are the sets of rational and irrational numbers equal?

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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.

These two sets together make up the set of real numbers.

Such numbers cannot be ordered in the manner suggested by the question because: For every whole number there are integers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every integer there are whole numbers, rational numbers, natural numbers, irrational numbers and real numbers that are bigger. For every rational number there are whole numbers, integers, natural numbers, irrational numbers and real numbers that are bigger. For every natural number there are whole numbers, integers, rational numbers, irrational numbers and real numbers that are bigger. For every irrational number there are whole numbers, integers, rational numbers, natural numbers and real numbers that are bigger. For every real number there are whole numbers, integers, rational numbers, natural numbers and irrational numbers that are bigger. Each of these kinds of numbers form an infinite sets but the size of the sets is not the same. Georg Cantor showed that the cardinality of whole numbers, integers, rational numbers and natural number is the same order of infinity: aleph-null. The cardinality of irrational numbers and real number is a bigger order of infinity: aleph-one.

Because irrational numbers are defined as those that are not rational. The dichotomy means that every real number belongs to one or the other of these sets, and never to both.

Related questions

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

The real numbers.

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.)

The real 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.

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.

Numbers cannot be rational and irrational at the same time.

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.

These two sets together make up the set of real numbers.

Together, the two sets comprise the set of real numbers.