I'm currently trying to learn Singular Homology from Munkres' book- "Elements of Algebraic Topology" . On page 173, theorem 30.7 appears: " If $f,g:(X,A) \to (Y,B) $ are homotopic, then $f _ * = g_* $ "
The author finishes the proof by showing that $ \partial D = f_\#-g_\#- D \partial$
Can someone explain me why it finishes the proof?
Thanks in advance !