Close, but no cigar. It's true to say that there exist many irrational numbers which are seperated by an infinite number of rational numbers. But not that there are an infinite number of rational numbers between any two irrational numbers, since there are irrational number between which zero rational numbers exist, between which one exists, between which two exist, etc..

Close, but no cigar. It's true to say that there exist many irrational numbers which are seperated by an infinite number of rational numbers. But not that there are an infinite number of rational numbers between

any twoirrational numbers, since there are irrational number between which zero rational numbers exist, between which one exists, between which two exist, etc..