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Let f : R to R be the signum function d...

Let `f : R to R` be the signum function defined as `f(x) = {{:(1, x gt 0),(0, x =0),(-1, x lt 0):}` and `g: R to R` be the greatest integer function given by `g(x) = [x]` where [x] is greatest integer less than or equal to x. Then, does fog and gof coincide in (0,1] ?

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