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No, only for Irrational Numbers.
Actually, that's not true.
Take any two rationals, a/b and c/d where a,b,c,d are integers and b,d are nonzero.
The average of a/b and c/d is (ad+bc)/2bd. This is a rational number between a/b and c/d.
Now take the average of this new number and the first number. This gives you:
(2abd+abd+cb^2)/(2db^2)
which is rational and also between the first and third number.
We could carry on this process ad infinitum. We would then have an infinite collection of numbers between a/b and c/d.
Hence the answer is yes.
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What is the states that an infinite number of rational numbers can be found between any two rational numbers?
That is the property of infinite density of rational numbers. If x and y are any two rational numbers then w = (x + y)/2 is a rational number between them. And then there is a rational number between x and w. This process can be continued without end.
How many rational numbers can be put between 2 and7?
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.
Is there rational numbers than irrational?
There are infinitely many rational numbers and irrational numbers but the cardinality of irrationals is larger by an order of magnitude.If the cardinality of the countably infinite rational numbers is represented by a, then the cardinality of irrationals is 2^a.
Are all number between 1 and 2 rational numbers?
No, there are more irrational numbers between 1 and 2 than there are rational numbers.
Are all numbers between 1 and 2 rational numbers?
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
