A function is increasing on A if f(x)<=f(y) for all x <y in A. Show that the intermediate value theorem does have a converse if we assume f is increasing on [a,b].
We'll prove this by contradiction.
Suppose that f is not continuous and let a<c<b.
Let e>0 .Since f is ...
The Intermediate Value Theorem is proven not to have a converse over a given interval. The solution is concise.