Infix notation : Usage, Further notations, Order of operations Wikipedia, the free encyclopedia

Infix notation

Mathematics notation with operators between operands

Postfix notation
("Reverse Polish")

Infix notation

Prefix notation
("Polish")

Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in 2 + 2.

Usage

Binary relations 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 lines a and b are denoted $a\perp b\ ,$ and in projective geometry two points b and c are in perspective when $b\ \doublebarwedge \ c$ while they are connected by a projectivity when $b\ \barwedge \ c.$

Infix notation is more difficult to parse by computers than prefix notation (e.g. + 2 2) or postfix notation (e.g. 2 2 +). However many programming languages use it due to its familiarity. It is more used in arithmetic, e.g. 5 × 6.^[1]

Further notations

Infix notation may also be distinguished from function notation, where the name of a function suggests a particular operation, and its arguments are the operands. An example of such a function notation would be S(1, 3) in which the function S denotes addition ("sum"): S(1, 3) = 1 + 3 = 4.

Order of operations

In infix notation, unlike in prefix or postfix notations, 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.