Editing Function (mathematics) (section)

=== Index notation ===

Index notation may be used instead of functional notation. That is, instead of writing {{math|''f''{{hair space}}(''x'')}}, one writes <math>f_x.</math>

This is typically the case for functions whose domain is the set of the [[natural number]]s. Such a function is called a [[sequence (mathematics)|sequence]], and, in this case the element <math>f_n</math> is called the {{mvar|n}}th element of the sequence.

The index notation can also be used for distinguishing some variables called ''[[Parameter (mathematics)|parameter]]s'' from the "true variables". In fact, parameters are specific variables that are considered as being fixed during the study of a problem.  For example, the map <math>x\mapsto f(x,t)</math> (see above) would be denoted <math>f_t</math> using index notation, if we define the collection of maps <math>f_t</math> by the formula <math>f_t(x)=f(x,t)</math> for all <math>x,t\in X</math>.