Well a function which is continuous is a function which is continuous everywhere. A non-continuous function is a function with at least one discontinuity. Is this what you want, or do you want a function which is nowehere continuous?
Hi I was wondering if anyone could point me in the right direction here:
I need an example of a function f:[a,b] --> R that is not continuous but whose range is:
(a) an open and bounded interval
(b) an open and UNbounded interval
(c) a closed and unbounded interval.
Thanks for any help
Regarding:
This function is closed and bounded isnt it? I was just wondering because you said it worked for (b) and (c). I can see that f(x)=tan(x) by itself has a range which is open and bounded, but I dont see how including the f(x)=0 at x=-pi/2 and x=pi/2 would make it an open interval...
I had to pick arbitrary values for because tan(x) isn't defined there, but f(x) had to be defined on a closed interval (so excluding the endpoints from the domain wasn't an option).
The range is , which is both open and closed (sometimes called "clopen") and clearly unbounded.