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## Homework Statement

I have to find f: R [tex]\rightarrow[/tex] R which is discontinuous at the points of the set {1/n : n a positive integer}[tex]\cup[/tex] {0} but continuous everywhere else.

Also find g: R [tex]\rightarrow[/tex] R which is discontinuous at the points of the set {1/n : n a positive integer}but continuous everywhere else.

## Homework Equations

## The Attempt at a Solution

Could I define f as f(x) = 1/(integer(x) -1) for x [tex]\in[/tex] [0,1) (where integer means round up to next integer), f(x) = x otherwise.

Similarly for g, can I say g(x) = 1/(integer(x) -1) for x [tex]\in[/tex] (0,1) (where integer means round up to next integer), g(x) = x otherwise.

I'm not too sure about these functions but cannot think of any more 'normal' ones that would satisfy the criteria.