# Discontinuity at certain points

1. May 25, 2010

### rainwyz0706

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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!

2. May 25, 2010

### HallsofIvy

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

3. May 25, 2010

### 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.