Standard (mathematics)

From Citizendium
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Discussion
Definition [?]
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.
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
  • In set theory, standard model of the natural numbers usually refers to the set 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.