Definition:Identity Mapping/Also known as

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The identity mapping can also be seen referred to as the identity operator, identity function or identity transformation.

Alternative symbols for $I_S$ include $1_S$, $i_S$, $j_S$, $id_S$, $\operatorname {id}_S$, $\operatorname {Id}_S$, $\iota_S$ and $\varepsilon_S$.

The subscript is frequently removed if there is no danger of confusion as to the domain under discussion.

Some sources use the same symbol for the identity mapping as for the inclusion mapping without confusion, on the grounds that the domain and codomain of the latter are different.

As the identity mapping is (technically) exactly the same thing as the diagonal relation, the symbol $\Delta_S$ is often used for both.