Question

prove that the Dirichlet function is not continuous at x=0

Answer 1

the function states that for rational values it has 1 and for irrational values it has something else.
i'm not sure about the values but the proof goes like this.
take the left hand limit:
u see that the limit values oscillates between the 2 dirichilet values. around 0 , there's both rational and irrational values and hence LHL DNE. therefore limit doesnot exist. and hence it is dis=continiuos.

Answer 2

0 if x is irrational
1 if x is rational.

thanks :]