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**shilz222** But the definition of the limit (epsilon-delta) is based on $\displaystyle \mathbb {R}^{n} $? So we cant really use a definition of a limit that is defined in $\displaystyle \mathbb{R}^{n} $ in $\displaystyle \mathbb{Z}^{n} $ right? So basically when you take a limit in $\displaystyle \mathbb{Z}^{n} $ the closest you can be is 1 unit away. So cant you restrict the definition of a limit? You are still taking a limit right?

Actually I think you can. $\displaystyle \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset $ $\displaystyle \mathbb{R} $ by the Dedekind cuts. So the definition that applies in $\displaystyle \mathbb{R}^{n} $ will also apply to $\displaystyle \mathbb{Z}^{n} $ but not vice-versa.