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.
There are an infinite number of rational numbers between any two rational numbers.
Find the arithmetic average of the two rational numbers. It will be a rational number and will be between the two numbers.
There are [countably] infinite rational number between any two rational numbers. There is, therefore, no maximum.
Yes it will be. The set of real numbers can be divided into two distinct sets: rational and irrational. So if it is not rational, then it is irrational.
There are infinitely many rational numbers between any two rational numbers. And the cardinality of irrational numbers between any two rational numbers is even greater.
In between any two rational numbers there is an irrational number. In between any two irrational numbers there is a rational number.
In between any two rational numbers there is an irrational number. In between any two Irrational Numbers there is a rational number.
There is an infinite number of them between any two rational numbers.
Rational numbers form a proper subset of real numbers. So all rational numbers are real numbers but all real numbers are not rational.
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.
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.