Thread: Proof...monotonicity

Let f:[a,b]--->R be monotone. Prove that f has a limit at BOTH a and b.

I have no idea what to do. Please help. Thanks

Originally Posted by zhupolongjoe

Let f:[a,b]--->R be monotone. Prove that f has a limit at BOTH a and b.

Let's assume that is nondecreasing.
The set is bounded below by .
So let . Show that is limit as .

Ok, so do I just show that using the limit definition or is there some other trick?
After that, I assume I should make T={f(x): x is in (a,b)} bounded above by f(b)

And then have L2=sup(T) and show L2 is the limit as x--->b-?

Thanks