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.

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

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.

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".

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 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.

There are an infinite number of them. Here are two: 7.48000000001 7.48000000002

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.

Yes. Not only that, but there are an infinite number of rationals between any two distinct rationals - however close. We can prove it like this: Take any three rational numbers, call them A, B and C, where B is larger than A, and C is any rational number greater than 1: D = A + (B - A) / C That gives us another rational number, D, no matter what the values of the original numbers are.

Rational numbers are numbers that can be expressed as a fraction a/b where a and b are both integers and b is not equal to zero. All integers n are rational numbers because they can be expressed as the fraction n/1. Rational numbers are closed under addition, subtraction, multiplication and division by a non-zero rational. To be closed under addition, subtraction, multiplication and division by a non-zero rational means that if you have two rational numbers, when you add, subtract, multiple or divide them, you will get another rational number. For example, take the rationals 1/3 and 4/3. When you add them together, you get another rational number, 5/3. Same with the other operations. 1/3 - 4/3 = -1 (remember integers are rational, too) (1/3) * (4/3) = 4/9 (1/3) / (4/3) = 1/4

8.3 and 8.26 are both rational numbers. Their sum is 16.56. That's also a rational number. Their difference is 0.04. That's also a rational number. Their product is 68.558. That's also a rational number. Their quotient is close to 0.9952. It can't be completely written as a decimal, but it's equivalent to 413/415 and it's a rational number too.

Roughly speaking, rational numbers can form real numbers that's why they are more densed than real numbers. For example, if A is a subset of some set X & every point x of X belongs to A then A is densed in X. Also Cauchy sequence is the best example of it in which every bumber gets close to each other hence makes a real number.

smaller

The link below is as close as I can find, it is not a complete list though.

cardinal (1, 2, 3, ...) and ordinal (1st, 2nd, 3rd, ...)or rational and irrationalA rational number can be expressed as a fractionex: 22/7 is roughly 3.14, very close to pi, but not pi which is still real but...Irrational - it cannot be expressed in the form of a fraction, other irrational numbers: sqrt(2), e.

15 ,67, and 84 are numbers that are close to the given numbers to make estimation easier.

The answer depends on what w represents. If w is the denominator of the rational function then as w gets close to zero, the rational function tends toward plus or minus infinity - depending on the signs of the dominant terms in the numerator and denominator.

The numerator is "much smaller" than the denominator. "Much smaller" is subjective, but then so is "close to" in the question.

The two numbers add up close to 5.5, but not exactly.

There are infinitely many rational numbers between any two rational numbers - no matter how close you try to make them. 4/7 = 36/63 = 360/630 and 5/9 = 35/63 = 350/630 So 351/630, 352/360, ..., 359/630 are between the two. As are 3511/3600, 3512/3600 etc and 35111/36000, 35112/36000 and so on.