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Math Help - Discontinuities of step functions

  1. #1
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    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.
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  2. #2
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    This is no "deep" property of continuity- just counting. Consider what happens when phi and gamma are discontinuous at the same point.
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