Does the following function have a limit as x approaches a?
$f(x) = 0$ if x is irrational, $f(x) = 1$ if x is rational.
Answers given in terms of delta-epsilon please!
My thoughts so far:
(1.) Its graph seems to show this function acting as though it were two constant functions
(2.) Between any two rational numbers there are infinitely many rational numbers; between any two rational numbers there are infinitely many irrational numbers. So I cannot think of any interval where rational numbers wouldn't interrupt irrational numbers, or irrational numbers interrupt rational numbers.
I'm sorry to have so little to add to the question. This is just one of those functions which goes beyond anything you've learned.