Example · High school
Terms
| Term | This example | Why |
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| identity function |
✓ |
The function $g : [0, 1] \to [0, 1]$ defined by $g(x) = x$ is the identity function on $[0, 1]$, because $g$ sends each point of $[0, 1]$ to itself and its codomain is its domain. It is a different function from the identity function on $\reals$, because its domain is different.
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| inclusion map |
✓ |
The function $g : [0, 1] \to [0, 1]$ defined by $g(x) = x$ is the inclusion map of $[0, 1]$ into itself, because $[0, 1]$ is a subset of itself and $g$ sends each point to itself.
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