Groups and Composition
For Translations:
- There exists an inverse mapping for each function
- There exists an identity mapping
These properties might seem trivial at first glance, but they are
actually very important, because when these conditions are shown
for any class of functions it can be proven that such a class is
closed under composition (i.e. any series of translations can be
composed to a single translation). In mathematical parlance this
the same as saying that translations form an algebraic group.
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