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Are these two mathematical objects the same from a practical standpoint, or literally identical mathematical objects? [closed]

This question is derived from another question that I recently asked. Take the two mathematical objects $\{ \mathbf{x} \in \mathbb{R}^n \mid x_1, x_2, \ldots, x_n \in \mathbb{Z} \}$ and $\{ \mathbf{x}...
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