Yes, there are infinitely many of them!
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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.
There is an infinite number of them 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.
There are an infinite number of rational numbers between any two given numbers.
-- Every whole number is a rational number. -- Any whole number divided by any whole number (except zero) produces a rational number.