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 (usually) larger range.

Clearly if $$T = S$$ then $$i: S \to S = I_S$$ which is the identity mapping on $$S$$

Notation
Beware the notation used. Always be sure you understand what is being used.

Some authors use $$i$$ (or similar) for the identity mapping, and so use something else, probably $$\iota$$, for the inclusion mapping.