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