<Dl> <Dd> f (x) = (1 x rational 0 x irrational (\ displaystyle f (x) = (\ begin (cases) 1&x (\ text (rational)) \ \ 0&x (\ text (irrational)) \ end (cases))) </Dd> </Dl> <Dd> f (x) = (1 x rational 0 x irrational (\ displaystyle f (x) = (\ begin (cases) 1&x (\ text (rational)) \ \ 0&x (\ text (irrational)) \ end (cases))) </Dd> <P> (the Dirichlet function) has no limit at any x-coordinate . </P> <Dl> <Dd> f (x) = (1 for x <0 2 for x ≥ 0 (\ displaystyle f (x) = (\ begin (cases) 1& (\ text (for)) x <0 \ \ 2& (\ text (for)) x \ geq 0 \ end (cases))) </Dd> </Dl>

When does the limit of a function exist