Difference between revisions of "Identity"
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| − | Let $X$ be any set. The function $\mathrm{id} \colon X \rightarrow X$ defined by $\mathrm{id}(x)=x$ is called the identity | + | Let $X$ be any set. The function $\mathrm{id} \colon X \rightarrow X$ defined by $\mathrm{id}(x)=x$ is called the identity on $X$. |
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
File:Identityplot.png|Plot of $\mathrm{id}$ with $X=\mathbb{R}$. | File:Identityplot.png|Plot of $\mathrm{id}$ with $X=\mathbb{R}$. | ||
| − | File:Complexidentityplot.png|[[Domain coloring]] of $\mathrm{id}$. | + | File:Complexidentityplot.png|[[Domain coloring]] of $\mathrm{id}$ with $X=\mathbb{C}$. |
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | =Properties= | ||
| + | |||
| + | =References= | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 23:02, 25 December 2016
Let $X$ be any set. The function $\mathrm{id} \colon X \rightarrow X$ defined by $\mathrm{id}(x)=x$ is called the identity on $X$.
Plot of $\mathrm{id}$ with $X=\mathbb{R}$.
Domain coloring of $\mathrm{id}$ with $X=\mathbb{C}$.
