Does this give a verry strong hint?
Prove that the function f defined by if is rational and if x is irrational is continuous at 0 only .
Ok so I was thinking doing it this way:
such that , , and
such that , , and
Then,
So then if I say something like there exists a sequence of rational numbers such that and a sequence of irrational number such that . And then show that there limits are the same would that show that it is only continuous at 0???
Yes, it does give a strong hint...
Ok so how would I word my answer??? Would something like that be correct?
Let Choose .
Then for ,
This shows that the function is continous at 0 but it doesn't show that it is only at 0, right???
So I have to show that the function is discontinuous at every other points? If I showed that there are two sequences converging to different limit would that be enough?