section_path: Notation/Dot notation
section_name: Dot notation
paragraph_text: Dot notation
  
  In the notation x ↦ f (x), {\displaystyle x\mapsto f(x),} the symbol x does not represent any value; it is simply a placeholder, meaning that, if x is replaced by any value on the left of the arrow, it should be replaced by the same value on the right of the arrow. Therefore, x may be replaced by any symbol, often an interpunct " ⋅ ". This may be useful for distinguishing the function f (⋅) from its value f (x) at x.
  
  For example, a (⋅) 2 {\displaystyle a(\cdot)^{2}} may stand for the function x ↦ a x 2 {\displaystyle x\mapsto ax^{2}}, and ∫ a (⋅) f (u) d u {\textstyle \int _{a}^{\,(\cdot)}f(u)\,du} may stand for a function defined by an integral with variable upper bound: x ↦ ∫ a x f (u) d u {\textstyle x\mapsto \int _{a}^{x}f(u)\,du}.