My teacher tells me that in the vicinity of any rational number, an irrational exists. To elucidate, I presume, he further went on to say, if a function, if defined to give 1 for every rational number and 0 for every irrational, then the function would be discontinuous at each and every point.
So that means that there are two irrational numbers surrounding a rational, right? And vice versa? So if I take the A.M. of those two irrational numbers, I get a rational number? Or of those two rational numbers, an irrational? Does that make sense?