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Yes. The infinity of rational numbers has the same size as the natural numbers, said to be "countable". The infinity of real numbers (and therefore, also of Irrational Numbers) is a larger infinity, said to be "uncountable".
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoYes. Although the sets of rational and irrational numbers are both infinite, the cardinality of irrational number is larger by an order of magnitude. If the number of rationals, which is countable infinite, is represented by a, then the number of irrationals is 2^a.
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Are there fewer rational numbers than irrational numbers?
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.
What is the number of rational numbers between square root 3 and square root 5?
Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.
Are there more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
How are rational and irrational numbers similar?
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.)
Are there more rational number than irrational numbers?
There are more irrational numbers than rational numbers. The rationals are countably infinite; the irrationals are uncountably infinite. Uncountably infinite means that the set of irrational numbers has a cardinality known as the "cardinality of the continuum," which is strictly greater than the cardinality of the set of natural numbers which is countably infinite. The set of rational numbers has the same cardinality as the set of natural numbers, so there are more irrationals than rationals.
There are fewer rational numbers than irrational numbers.?
Yes, there are.
Is There are fewer rational than irrational numbers?
Yes, fewer by an order of infinity.
Do irrational numbers contain fewer numbers?
No, the set of irrational numbers has a cardinality that is greater than that for rational numbers. In other words, the number of irrational numbers is of a greater order of infinity than rational numbers.
Are there fewer rational numbers than irrational numbers?
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.
List of rational and irrational numbers?
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
What is the number of rational numbers between square root 3 and square root 5?
Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.
Are there more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
Are more rational numbers than irrational numbers true or false?
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
How are rational and irrational numbers similar?
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.)
Is there more rational numbers then irrational?
No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.
Which numbers is not rational?
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Is there inifinitely many irrational numbers?
Yes. In fact, the cardinality of irrational numbers is greater than that of rational numbers.
