Identity map

Definition

The "identity map", written on this project as [ilmath]\text{Id} [/ilmath], is a map which maps every item (in the domain) to itself, that is if [ilmath]\text{Id}:X\rightarrow X[/ilmath] is a function / map on some set [ilmath]X[/ilmath], then:

• [ilmath]\forall x\in X[\text{Id}(x)\eq x][/ilmath]

Conventions

If we are dealing with two sets [ilmath]X[/ilmath] and [ilmath]Y[/ilmath], then technically we must use differing notation for the identity map on each, for example [ilmath]\text{Id}_X[/ilmath] and [ilmath]\text{Id}_Y[/ilmath] however this is rarely needed and we (even I, Alec) usually just write [ilmath]\text{Id} [/ilmath] for both

Other notations

Sometimes [ilmath]I[/ilmath] is used for the identity map.

References

Grade: D

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Not really important Alec (talk) 15:04, 15 December 2017 (UTC)