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Q: Name two rational numbers that are close to but smaller than each of the rational numbers given below?

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There are infinitely many rational numbers between any two rational rational numbers (no matter how close).

There are infinitely many rational numbers between any two rational numbers - no matter how close together they are.

There are infinitely many rational numbers between any two (different) numbers, no matter how close together they are.

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.

The idea is to look for a rational number that is close to the desired irrational number. You can find rational numbers that are as close as you want - for example, by calculating more decimal digits.

Every fraction is a rational number, as long as it has whole numbers on topand bottom. In fact, that's very close to the definitionof a rational number.

Numbers are infinitely dense. Between any two rational or real numbers, no matter how close, there are infinitely many numbers.

There is no such number. The given number is rational and rational numbers are infinitely dense. Between any two rational numbers - no matter how close together - there are an infinite number of rational numbers. That means, whatever number you propose as the "next" number, there are infinitely many numbers between 984339.78 and your proposed number. So it cannot be the "next".

You cannot. The diagonal of a unit square cannot be represented by a rational number. However, because rational numbers are infinitely dense, you can get as close to an irrational number as you like even if you cannot get to it. If this approximation is adequate than you are able to represent the real world using rational numbers.

No.Try to created a table or a graph for the equation:y = 0 when x is rational,andy = 1 when x is irrational for 0 < x < 1.Remember, between any two rational numbers (no matter how close), there are infinitely many irrational numbers, and between any two irrational numbers (no matter how close), there are infinitely many rational numbers.

There are an infinite number of rational numbers between any two rational numbers. And 2 and 7 are rational numbers. Here's an example. Take 2 and 7 and find the number halfway between them: (2 + 7)/2 = 9/2, which is rational. Then you can take 9/2 and 2 and find a rational number halfway: 2 + 9/2 = 13/2, then divide by 2 = 13/4. No matter how close the rational numbers become, you can add them together and divide by 2, and the new number will be rational, and be in between the other 2.

Infinitely many. The set of rational numbers (as well as irrationals) are infinitely dense. This means that no matter how close you pick two rational numbers, there are infinitely many rational numbers between them. And if you pick any two of those, there are infinitely many between those two.

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