How to prove that Dirichlet function has no limit?
Take ε = 1 / 2
There are both rational and irrational numbers in any open interval
Then the absolute value of the difference of function values is 1 > 1 / 2
So there is no limit
Take ε = 1 / 2
There are both rational and irrational numbers in any open interval
Then the absolute value of the difference of function values is 1 > 1 / 2
So there is no limit