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Q: Is infinity a rational number

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1/infinity? * * * * * Nice idea but unfortunately that is not a rational number, which is defined as the ration of two integers, x/y where y > 0. Since infinity is not an integer, the suggested ratio is not a rational number. The correct answer is that there is no such number. If any number laid claim to being the smallest positive rational, then half of that number would have a better claim. And then a half of THAT number would be a positive rational that was smaller still. And so on.

It is a rational number

yes

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.

Yes.

Related questions

Infinity

Infinitely rarely, a real number is also a rational number. (There are an infinite number of rational numbers, but there are a "much bigger infinity" of real numbers.)

1/infinity? * * * * * Nice idea but unfortunately that is not a rational number, which is defined as the ration of two integers, x/y where y > 0. Since infinity is not an integer, the suggested ratio is not a rational number. The correct answer is that there is no such number. If any number laid claim to being the smallest positive rational, then half of that number would have a better claim. And then a half of THAT number would be a positive rational that was smaller still. And so on.

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).

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

Yes. A real number is any comprehendable number, from negative infinity to positive infinity. A rational number is any number that can be the answer to a division equation; an integer, fraction, or a decimal. An irrational number is any number that cannot be expressed as a fraction; such as exponents.

There are countably infinite rational numbers. That is, it is possible to map each rational number to an integer so that the set has the same number of elements as all integers. This is the lowest order or infinity, Aleph-null. The number of irrationals is a higher order of infinity: 2^(Aleph-null). This is denoted by C, for continuum. There are no orders of infinity between Aleph-null and C.

No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.

To divide any number by zero will give infinity and therefore an error.

Yes, any number whose decimal terminates or has repeating decimals to infinity is a rational number. More precisely, any number that can be expressed as a fraction between two integers is a rational number. In this case 100000000000.2 = 1000000000002/10, or 500000000001/5.

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".

A rational number can be expressed as a fraction a/b, where a and b are integers. This includes the integers themselves, that can be expressed as (number) / 1. An irrational number is one that can't be exactly expressed in this way. This includes the square roots of any integer that is not a perfect square; pi; and e - and a host of other numbers. There are more rational than irrational numbers (rational numbers are a countable infinity", and irrational numbers an "uncountable infinity"), but we usually deal mainly with rational numbers - or use rational approximations for the numbers we deal with.

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