I'm not sure how to go about it.

[neoking77]

Let f be the function that takes the value of 1 on all rational numbers, and 0 on all irrational numbers. At what points is f continuous?

Does anyone know how to do this?? I mean, there are just so many points to point out...such as square root of 2 and 10, and the list is endless...

 

[genneth]

I'm fairly sure it's not continuous anywhere. Specifically, for any neighbourhood about any point, will contain some rationals and some irrationals, and so a sequence of decreasing neighbourhoods don't converge to any value.

 

[neoking77]

I see! Thanks a lot!