Definition:Inclusion Mapping

The inclusion mapping $$i: S \to T$$ is a mapping on a set $$S$$ defined when $$S \subseteq T$$:

$$i: S \to T : i \left({s}\right) = s$$

It can be seen that the inclusion mapping is similar to the identity mapping, except has a larger range. In fact, it can be seen that:

$$i: S \to \mathrm{Im} \left({i}\right) = I_S$$