Editing Function composition (section)

==Alternative notations==
Many mathematicians, particularly in [[group theory]], omit the composition symbol, writing {{math|''gf''}} for {{math|''g'' ∘ ''f''}}.<ref name="Ivanov_2009"/>

During the mid-20th century, some mathematicians adopted [[postfix notation]], writing {{math|''xf''&thinsp;}} for {{math|''f''(''x'')}} and {{math|(''xf'')''g''}} for {{math|''g''(''f''(''x''))}}.<ref name="Gallier_2011" /> This can be more natural than [[prefix notation]] in many cases, such as in [[linear algebra]] when {{mvar|x}} is a [[row vector]] and {{mvar|f}} and {{mvar|g}} denote [[matrix (mathematics)|matrices]] and the composition is by [[matrix multiplication]]. The order is important because function composition is not necessarily commutative. Having successive transformations applying and composing to the right agrees with the left-to-right reading sequence.

Mathematicians who use postfix notation may write "{{math|''fg''}}", meaning first apply {{mvar|f}} and then apply {{mvar|g}}, in keeping with the order the symbols occur in postfix notation, thus making the notation "{{math|''fg''}}" ambiguous. Computer scientists may write "{{math|''f'' ; ''g''}}" for this,<ref name="Barr-Wells_1990"/> thereby disambiguating the order of composition. To distinguish the left composition operator from a text semicolon, in the [[Z notation]] the ⨾ character is used for left [[relation composition]].<ref name="ISOIEC13568"/> Since all functions are  [[Binary relation#Special types of binary relations|binary relations]], it is correct to use the [fat] semicolon for function composition as well (see the article on [[composition of relations]] for further details on this notation).