Infix notation is the notation commonly used in

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

al and

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from prem ...

al formulae and statements. It is characterized by the placement of operators between

operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above exam ...

s—" infixed operators"—such as the

plus sign The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, res ...

in .

Usage

Binary relation In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over sets and is a new set of ordered pairs consisting of elements in and in ...

s are often denoted by an infix symbol such as

set membership In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set. Sets Writing A = \ means that the elements of the set are the numbers 1, 2, 3 and 4. Sets of elements of , for example \, are subsets o ...

''a'' ∈ ''A'' when the set ''A'' has ''a'' for an element. In

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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 language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming ...

s use it due to its familiarity. It is more used in arithmetic, e.g. 5 × 6.

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"): .

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 In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For examp ...

References

{{Reflist

External links

''RPN or DAL? A brief analysis of Reverse Polish Notation against Direct Algebraic Logic''Infix to postfix convertor
' ic' Mathematical notation Operators (programming)

Usage

Further notations

Order of operations

See also

References

External links