## Quick Reference

A mapping (or function) *f* from *S* to *T*, where *S* and *T* are non-empty sets, is a rule which associates, with each element of *S*, a unique element of *T*. The set *S* is the domain and *T* is the codomain of *f*. The phrase ‘*f* from *S* to *T*’ is written ‘*f*: *S* → *T*’. For *s* in *S*, the unique element of *T* that *f* associates with *s* is the image of *s* under *f* and is denoted by *f*(*s*). If *f*(*s*)=*t*, it is said that *f* maps *s* to *t*, written *f*: *s* ↦ *t*. The subset of *T* consisting of those elements that are images of elements of *S* under *f*, that is, the subset { *t* | *t*=*f*(*s*), for some *s* in *S*}, is the image (or range) of *f*, denoted by *f*(*S*). For the mapping *f*: *S* → *T*, the subset {(*s*, *f*(*s*) | *s* ∈ *S*} of the Cartesian product *S*×*T* is the graph of *f*. The graph of a mapping has the property that, for each *s* in *S*, there is a unique element (*s, t*) in the graph. Some authors define a mapping from *S* to *T* to be a subset of *S*×*T* with this property; then the image of *s* under this mapping is defined to be the unique element *t* such that (*s, t*) is in this subset.

*Subjects:*
Mathematics.

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