Identity

Let $X$ be any set. The function $\mathrm{id} \colon X \rightarrow X$ defined by $\mathrm{id}(x)=x$ is called the identity function on $X$.

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  Plot of $\mathrm{id}$ with $X=\mathbb{R}$.

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  Domain coloring of analytic continuation of $\mathrm{id}$ with $X=\mathbb{C}$.