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Let f : R rarr R be the signum function...

Let f : R `rarr` R be the signum function defined as f(x)= `{{:(1,x gt0),(0,x=0),(-1,x lt0):}` and g :R `rarr` be the greatest integer function given by g(x) = [x] . Then prove that fog and gof coincide in [-1,0).

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