Originally Posted by
MatthewD Sorry for not being more descriptive, but the functions are not supposed to be constant--I apologize for neglecting to post that!
I see what you're saying: since 1/(x-1) is unbounded, it is not integrable on [0,1]. Correct? Is it enough to say that, or do I need to bring in 2 partitions converging to different points?
Just curious, for the function f(x):=1 if x rat, f(x):=-1 if x irrat, since it is clearly bounded, wouldn't I have to talk about 2 different partitions? It's frustrating because I know it's not integrable, but since we are only working with Riemann integrable functions and their proofs, I'm not sure what I'm allowed to use: right now we're doing everything with partitions... any ideas?
I really appreciate your help!