Irrational Numbers

# Are there more rational numbers than irrational numbers true or false?

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In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.

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## Related Questions

-- 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.

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.

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. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.

Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).

A rational number is one that can be expressed as the ratio of two integers. There are an infinite number of both rational and irrational numbers, but there are more irrational numbers than rational ones... infinitely more, in fact.

Infinitely many. In fact, between any two different real numbers, there are infinitely many rational numbers, and infinitely many irrational numbers. (More precisely, beth-zero rational numbers, and beth-one irrational numbers - that is, there are more irrational numbers than rational numbers in any such interval.)

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 &Atilde;&euro;0 (Aleph-null) while the cardinality of the set of irrational numbers is 2&Atilde;&euro;0.

There are more irrational numbers between any two rational numbers than there are rational numbers in total.

Because it's an irrational number, and that's what "irrational" means. There are lots of other irrational numbers, like the base of the natural logarithm e or the square root of 2.In fact, there are more irrational numbers than rational numbers. A lot more.Infinitely more, even. There are an infinite number of rational numbers, but the infinite number of irrational numbers is a higher infinity than the infinity of rational numbers.

No. In fact, there are infinitely more irrational numbers than there are rational numbers.

The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.

Yes. There are more irrational real numbers than rational real numbers - an order of infinity more.

No. Although the count of either kind of number is infinite, the cardinality of irrational numbers is an order of infinity greater than for the set of rational numbers.

Any number is NOT rational. In fact, there are more irrational numbers than there are rational.

Yes. The rational numbers are countable, that is they can be put in a one-to-one correspondence with the counting numbers, but the irrational numbers cannot and so are not countable. There is a higher infinity of irrational numbers than the infinity of rational numbers.

No. The set of real numbers contains an infinitely more irrational numbers than rational numbers.

Actually there are more irrational numbers than rational numbers. Most square roots, cubic roots, etc. are irrational (not rational). For example, the square of any positive integer is either an integer or an irrational number. The numbers e and pi are both irrational. Most expressions that involve those numbers are also irrational.

Infinitely many! There are an infinite number of rational numbers between any two irrational numbers (they will more than likely have very large numerators and denominators), and there are an infinite number of irrational numbers between any two rational numbers.

5.68 is rational. All decimal numbers that terminate, or end in one or more repeating digits are rational numbers.

No, whole numbers are never irrational. There is nothing more rational than a whole number.

They are not rational, that is, they cannot be expressed as a ratio of two integers.Their decimal equivalent is infinitely long and non-recurring.Together with rational numbers, they form the set of real numbers,Rational numbers are countably infinite, irrational numbers are uncountably infinite.As a result, there are more irrational numbers between 0 and 1 than there are rational numbers - in total!

No, the set of irrationals has a greater cardinality.

No. The number of irrationals is an order of infinity greater.

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