can-a-function-f-n-R-R-be-such-that-n-0-f-n-x-converge-for-x-Q-and-diverge-for-x-R-Q-

Question Number 1462 by 123456 last updated on 07/Aug/15

can a function f_{n} : R \to R be such that

\underset{n = 0}{\sum^{+ \infty}} f_{n} (x) converge for x \in Q and diverge

for x \in R ∖ Q ?

Commented by prakash jain last updated on 08/Aug/15

The generic nature of this question allows

for direct examples such as

f_{n} (x) = {\begin{cases} g_{n} (x) & x \in Q \\ h_{n} (x) & x \in R ∖ Q \end{cases}

Commented by 123456 last updated on 09/Aug/15

what if f_{n} have to be continuous ?

Facebook Tweet Pin