There are an infinite number of numbers between any two numbers. It is very easy to prove, add 2+3 and divide it by 2, you would get 5/2, right? Now you can add 2 + 5/2 and divide it by 2, and 5/2 + 3 and divide it by 2. And so on, and so forth.
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No, there are more irrational numbers between 1 and 2 than there are rational numbers.
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!
There are infinitely many rational numbers between any two (different) numbers, no matter how close together they are.
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.
All rational numbers are fractional but all fractional numbers are not rational. For example, pi/2 is fractional but not rational.