Thread: Discontinuities of step functions

Hi, i'm rather stuck on an Analysis question so any help would be appreciated.

Let phi and gamma be step functions, and hence 9phi)+(gamma) is a step function [a,b] to R. By writing z(phi) for the number of discontinuities of phi. Prove or disprove:

-z((phi)+(gamma)) is less than or equal to z(phi) + z(gamma)

-z((phi)+(gamma)) is greater than or equal to max{z(phi),z(gamma)}

Thanks.

This is no "deep" property of continuity- just counting. Consider what happens when phi and gamma are discontinuous at the same point.