Discontinuity at certain points

[rainwyz0706]

Homework Statement

1.Find a function f : R → R which is discontinuous at the points of the set
{1/n : n a positive integer} ∪ {0} but is continuous everywhere else.
2. Find a function g : R → R which is discontinuous at the points of the set
{1/n : n a positive integer} but is continuous everywhere else.

Homework Equations

The Attempt at a Solution

I'm thinking of making f(x)=0 at points that f is discontinuous and f(x)=x everywhere else. But that only works for 2, not 1, right? Could anyone give me some hints? I'm not sure what the question is asking for. Thanks!

 

[HallsofIvy]

Why not just f(x)= 1 if x= 1/n for some positive integer n or x= 0, 0 otherwise?

 

[vaibhav1803]

only discontinuous..?
try, f(x) =[1/x]...where...[y] is the greatest integer less than or equal to y or as you would call, floor(y)...f(1/n) leads to a jump discontinuity one you can never fix, and hence an implied non-differentiability.