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{{Short description|Mathematics notation with operators between operands}}
{{Operator notation sidebar |logo=[[File:Infix-dia.svg|125px]]}}

'''Infix notation''' is the notation commonly used in [[arithmetic]]al and [[logic]]al formulae and statements. It is characterized by the placement of [[Operator (mathematics)|operator]]s between [[operand]]s—"infixed operators"—such as the [[plus sign]] in {{nowrap|2 '''+''' 2}}.

==Usage==
[[Binary relation]]s are often denoted by an infix symbol such as [[set membership]] ''a'' ∈ ''A'' when the set ''A'' has ''a'' for an element. In [[geometry]], [[perpendicular line]]s ''a'' and ''b'' are denoted <math>a \perp b \ ,</math> and in [[projective geometry]] two points ''b'' and ''c'' are in [[perspective (geometry)|perspective]] when <math>b \ \doublebarwedge \ c</math> while they are connected by a projectivity when <math>b \ \barwedge \ c .</math>

Infix notation is more difficult to [[parsing|parse]] by computers than [[prefix notation]] (e.g. '''+''' 2 2) or [[postfix notation]] (e.g. 2 2 '''+'''). However many [[programming language]]s use it due to its familiarity. It is more used in arithmetic, e.g. 5 '''×''' 6.<ref name="Infix, Postfix and Prefix">{{cite web | url=http://www.cs.man.ac.uk/~pjj/cs212/fix.html | title=The Implementation and Power of Programming Languages | access-date=30 August 2014 | archive-url=https://web.archive.org/web/20220827171346/https://www.cs.man.ac.uk/~pjj/cs212/fix.html | archive-date=27 August 2022}}</ref>

==Further notations==
Infix notation may also be distinguished from [[Function (mathematics)|function]] notation, where the name of a function suggests a particular operation, and its [[Argument of a function|arguments]] are the operands. An example of such a [[Function application|function notation]] would be {{math|S(1, 3)}} in which the function {{math|S}} denotes addition ("sum"): {{math|1=S (1, 3) = 1 + 3 = 4}}.

==Order of operations==
In infix notation, unlike in prefix or postfix notations, [[Bracket#Parentheses|parentheses]] surrounding groups of operands and operators are necessary to indicate the intended order in which operations are to be performed. In the absence of parentheses, certain precedence rules determine the [[order of operations]].

== See also ==
* [[Tree traversal]]: Infix (In-order) is also a tree traversal order. It is described in a more detailed manner on this page.
* [[Calculator input methods]]: comparison of notations as used by pocket calculators
* Postfix notation, also called [[Reverse Polish notation]]
* Prefix notation, also called [[Polish notation]]
* [[Shunting yard algorithm]], used to convert infix notation to postfix notation or to a tree
* [[Operator (computer programming)]]
* [[Subject–verb–object word order]]

==References==
{{Reflist}}

== External links ==
* [http://www.xnumber.com/xnumber/rpn_or_adl.htm ''RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic'']
*[https://web.archive.org/web/20130925214440/http://www.meta-calculator.com/learning-lab/how-to-build-scientific-calculator/infix-to-postifix-convertor.php Infix to postfix convertor]''[sic]''

[[Category:Mathematical notation]]
[[Category:Operators (programming)]]

Infix notation - Revision history

imported>Perception312: Undid revision 1276203550 by 2600:6C58:7F:46EE:C52C:2EF7:27EC:1C66 (talk)