Editing Function (mathematics) (section)

=== Dot notation ===

In the notation
<math>x\mapsto f(x),</math>
the symbol {{mvar|x}} does not represent any value; it is simply a [[placeholder name|placeholder]], meaning that, if {{mvar|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, {{mvar|x}} may be replaced by any symbol, often an [[interpunct]] "{{math| ⋅ }}". This may be useful for distinguishing the function {{math|''f''{{hair space}}(⋅)}} from its value {{math|''f''{{hair space}}(''x'')}} at {{mvar|x}}.

For example, <math> a(\cdot)^2</math> may stand for the function <math> x\mapsto ax^2</math>, and <math display="inline"> \int_a^{\, (\cdot)} f(u)\,du</math> may stand for a function defined by an [[integral]] with variable upper bound: <math display="inline"> x\mapsto \int_a^x f(u)\,du</math>.