If is increasing and satisfies the conclusion of the intermediate value theorem, then prove f is left continuous.
My attempt:
Hence pick and let s.t .
Let .
Also let (just to make it different from the definition).
therefore
Hence it is left continuous.
Is this right? I have a feeling that i've assumed it to prove it
Showcase, the intermediate value theorem says:
If f(x) is continuous in [a,b] and if f(a) =A and f(b)=B,then corresponding to any number C between A and B there exists at least one number c in [a,b] such that f(c) =C.
So it seems to me you are trying to prove the basic assumption of the intermediate value theorem,since if a function is continuous then is left,right continuous