A point x € E is a simple discontinuity (also called a discontinuity of the "first kind") for a function f on E if f(x-)

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A Point X E Is A Simple Discontinuity Also Called A Discontinuity Of The First Kind For A Function F On E If F X 1 (24.43 KiB) Viewed 9 times

A point x € E is a simple discontinuity (also called a discontinuity of the "first kind") for a function f on E if f(x-) and f(x+) exist and f is discontinuous at x. Prove that the set of simple discontinuities for a nondecreasing function f: R→ R is at most countable. Give an example of a real-valued function on [0, 1] with infinitely many simple discontinuitics.