By allowing the radix point to be adjustable, floating-point notation allows calculations over a wide range of magnitudes, using a fixed number of digits, while maintaining good precision.

Operator overloading is claimed to be useful because it allows the developer to program using notation " closer to the target domain " and allows user-defined types a similar level of syntactic support as types built into the language.

Once analyzed, a statement in prefix notation becomes less intimidating to the human mind as it allows some separation from convention with added convenience.

SMILES notation allows the specification of configuration at tetrahedral centers, and double bond geometry.

To simplify this problem, computer scientists have adopted Big O notation, which allows functions to be compared in a way that ensures that particular aspects of a machine's construction do not need to be considered, but rather only the asymptotic behavior as problems become large.

The compact notation allows many defaults and abbreviations for common cases.

B. F. Skinner, noted psychologist, commented on medical notation as a form of multiple audience control, which allows the doctor to communicate to the pharmacist things which might be opposed by the patient if they could understand it.

The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another.

It has a graphical notation and allows for extension with a Profile ( UML ).

The Iverson bracket allows the equivalent notation,, to be used instead of

The tetration notation allows us to make these diagrams slightly simpler while still employing a geometric representation ( we could call these tetration towers ).

Standard mathematical notation allows a formal definition of range.

* Encoding Control Notation, a standard notation that allows the specification of custom encoding rules for ASN. 1 types

Index notation allows indication of the elements of the array by simply writing a < sub > i </ sub >, where the index i is known to run from 1 to n.

The notation allows a clear generalization to multi-dimensional arrays of elements: tensors.

This allows the user to score parts using traditional notation, using the graphic notation of the piano roll and to record acoustic or electronic instruments in real time along side the existing scores.

SCORE is known for its ability to precisely position symbols on the page, and also allows the user complete control over every aspect of their music through making every possible aspect of music notation manually controllable ( this, however, also leads to some difficulty or frustration of use in the program ).

A VPL allows programming with visual expressions, spatial arrangements of text and graphic symbols, used either as elements of syntax or secondary notation.

The multi-index notation allows the extension of many formulae from elementary calculus to the corresponding multi-variable case.

Its generalization to binary notation allows to use it in a computer.

This kind of notation allows the use of quantum field theoretic techniques to be used in the analysis of reaction diffusion systems.

When a cubic graph is Hamiltonian, LCF notation allows it to be represented concisely.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

Let us clarify it by using modern-day notation.

To describe the construction let us fix some notation.

Before showing how to do this, let us simplify the notation.

Let us rewrite the preceding calculations in a more detailed notation which explicitly distinguishes random from not-random quantities ( that is a different distinction from the usual distinction in ordinary, deterministic, mathematics between variables and constants ).

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

Equivalently, some authors define the divergence of any mixed tensor by using the " musical notation #":

And the content of the " img " element is referencing another external entity " example1SVG " whose declaration also does not define an notation, so it will also be parsed by validating parsers and the entity replacement text will be located by its defined SYSTEM identifier " example1. svg " ( also interpreted as a relative URI ).

There are two formal ways to define each note and octave, the Helmholtz system and the Scientific pitch notation.

The notion, and notation, of " a class " ( set ): In the first edition PM asserts that no new primitive ideas are necessary to define what is meant by " a class ", and only two new " primitive propositions " called the axioms of reducibility for classes and relations respectively ( PM 1962: 25 ).

When Polish notation is used as a syntax for mathematical expressions by interpreters of programming languages, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same.

Because of this, Lisp ( see below ) and related programming languages define their entire syntax in terms of prefix notation ( and others use postfix notation ).

In modular arithmetic notation, define the function f as follows:

A common alternative notation is and for positive semidefinite and positive definite matrices, respectively .</ ref > The notion comes from functional analysis where positive-semidefinite matrices define positive operators.

Sigils have the notable advantages over Hungarian notation that they implicitly define the type of the variable without need for redundant declaration, and are also checked by the compiler, preventing omission and misuse.

A common abuse of notation is to define the del operator (∇) as follows in three-dimensional Euclidean space R < sup > 3 </ sup > with unit vectors:

People who communicate with technical drawings, ( those who design and those who are tradespeople ), may use technical standards that define practical symbols, perspectives, units of measurement, notation systems, visual styles, or layout conventions.

The product is in fact the same one used to define the product of polynomials in one indeterminate, which suggests using a similar notation.

To define a function, sometimes a dot notation is used in order to emphasize the functional nature of an expression without assigning a special symbol to the variable.

A notable semantic feature was the ability to define new data types, as a ( possibly recursive ) sum of products-this was done using a somewhat verbose natural language style description, but apart from notation amounts exactly to the algebraic data types found in modern functional languages.

It is necessary ( for the notation ) to choose an arbitrary orientation of the graph in order to define the cycle space, but the definition does not depend on that choice.

The goal of this section is to define a functor pt from Frm to Top that in a certain sense " inverts " the operation of Ω by assigning to each locale L a set of points pt ( L ) ( hence the notation pt ) with a suitable topology.

This notation is used in academic papers, but this does not define what " black " or " white " is in terms of colorimetry.

In Dirac notation, we define as the vacuum quantum state.

Using a more modern notation, define

The notation system consists of a combination of abbreviations and short forms of tricks and their direction slot system to define the direction and position of a trick.

# You cannot cleanly define what may mean, due to the fact the O notation is about growth of functions, but to the left hand and the right hand side of the relation, there are scalar values, and you cannot decide whether the relation holds if you look at particular function values.