# Definition:Identity Mapping/Also known as

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## Definition

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.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**identity mapping (identity function)** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**identity mapping (identity function)**