This has nothing to do with calculus and everything to do with the fact that there are an infinite number of irrational numbers between any two rational numbers

This has nothing to do with calculus and everything to do with the fact that there are an infinite number of irrational numbers between any two rational numbers. Indeed, if you randomly select a real number, you can be almost certain that you will select an irrational number. Of course, almost certain has a specific rigorous meaning: the probability of not selecting (in this case, an irrational number) is greater than zero, but less than all real numbers, i.e. Infinitesimal. Edit: spelling Edit: the infinitesimal belongs not in the real numbers, but in the hyperreal numbers, if you want to learn more