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Let ##G = \{x \in \mathbb{R} ~: 0 \le x < 1 \}##. Let ##x, y \in G##.I have to determine whether ##x \cdot y = x + y - \lfloor x + y \rfloor## is well-defined. However, it seems obvious. Since addition, subtraction, and the floor function are all well-defined functions in and of themselves, isn't it clear that the supposed operation in question is well-defined?