How could that not be the case? How many irrational numbers are there between [1, 2]? Infinitely many, of course. How many integers [0, 1, ...n] are there? Infi

How could that not be the case? How many irrational numbers are there between [1, 2]? Infinitely many, of course. How many integers [0, 1, ...n] are there? Infinitely many. Between every rational number there are infinitely many irrational numbers. If you now look at the whole numbers, including the irrational numbers in between, these are obviously "many more numbers".