Suppose \( f(x) = 1 \) when \( x \) is an irrational number
and \( f(x)=0 \) when \( x \) is rational. Find \( f(0) \) and \(
\lim_{x \to 0} f(x) \).
Suppose \( f(x) = 0 \) when \( x \) is an irrational number and \( f(x) = x^{2} \) when
\( x \) is rational. Find \( f(0) \) and \( \lim_{x \to 0} f(x) \).