Standard (mathematics)

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This editable Main Article is under development and subject to a disclaimer.

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This article is about the standard in mathematics. For other uses of the term standard, please see standard (disambiguation).

In mathematics, the word standard is often used in its non-technical sense to indicate the "normally" or "most frequently" used of several options. Words with a similar, but usually more formal and more technical meaning are: normal, natural, canonical. Thus there may be, for instance,

* a "standard" symbol that is usually (but not necessarily always) used, or
* a "standard" way to write an equation that need not be considered as a normal form.

Some very common examples for the use of the word "standard" are:

* The standard basis in d-dimensional real or complex vector spaces (or, more generally, in any d-dimensional vector space Kd over a field K)

is the basis formed by the d d-tuples

(1,0,…,0), (0,1,0,…,0),⋯,(0,…,0,1,0), (0,…,0,1)

* In set theory, standard model of the natural numbers usually refers to the set ℕ constructed inductively from the empty set.

* The term standard (natural, real, complex, etc.) numbers is used to distinguish the usually used numbers from their nonstandard counterparts.

* In statistics the standard deviation is the most commonly used measure of variation.

* In mathematical physics there is a well-known standard model of particle physics.