section_path: Notation/Index notation
section_name: Index notation
paragraph_text: Index notation
  
  Index notation may be used instead of functional notation. That is, instead of writing f (x), one writes f x. {\displaystyle f_{x}.}
  
  This is typically the case for functions whose domain is the set of the natural numbers. Such a function is called a sequence, and, in this case the element f n {\displaystyle f_{n}} is called the n th element of the sequence.
  
  The index notation can also be used for distinguishing some variables called parameters 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 x ↦ f (x, t) {\displaystyle x\mapsto f(x,t)} (see above) would be denoted f t {\displaystyle f_{t}} using index notation, if we define the collection of maps f t {\displaystyle f_{t}} by the formula f t (x) = f (x, t) {\displaystyle f_{t}(x)=f(x,t)} for all x, t ∈ X {\displaystyle x,t\in X}.