Definition:Translation Mapping/Caution

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Definition

It is easy to confuse the mappings $\tau_{\mathbf x}$ and $\tau_{-\mathbf x}$, and the choice made here is arbitrary.

The map $\tau_{\mathbf x}$ can be understood (appealing to our planar $\R^2$ intuition) as translating the coordinate axes by $\mathbf x$.