Question

Example for a function is not a sequence

Answer 1

Step-by-step explanation:

am trying to find a function f for which there does not exist a sequence of continuous functions fn converging pointwise to f.

I would be interested to see some examples. My first idea was the classic "very discontinuous functon" which is 0 at each rational and 1 at each irrational, but I believe it is possible to construct such a sequence fn because the rationals are countable. So I'm rather stuck. Maybe I need to find a subset of R which is dense, uncountable and not cocountable? In any case I would