Difference between revisions of "Constructive analysis"
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Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to [[separable spaces]]. | Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to [[separable spaces]]. | ||
| − | Also, some theorems may need to be approached by approximations. Furthermore, many classical theorems can be stated in ways that are logically equivalent according to [[classical logic]], but not all of these forms will be valid in constructive analysis, which uses [[intuitionistic logic]]. | + | Also, some theorems may need to be approached by [[Approximation|approximations]]. |
| + | |||
| + | Furthermore, many classical theorems can be stated in ways that are logically equivalent according to [[classical logic]], but not all of these forms will be valid in constructive analysis, which uses [[intuitionistic logic]]. | ||
== See also == | == See also == | ||
| + | * [[Approximation]] | ||
* [[Constructive mathematics]] | * [[Constructive mathematics]] | ||
* [[Intuitionistic logic]] | * [[Intuitionistic logic]] | ||
Revision as of 20:08, 17 February 2016
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.
Description
Constructive analysis contrasts with classical analysis, which (in this context) simply means analysis done according to the (ordinary) principles of classical mathematics.
Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to separable spaces.
Also, some theorems may need to be approached by approximations.
Furthermore, many classical theorems can be stated in ways that are logically equivalent according to classical logic, but not all of these forms will be valid in constructive analysis, which uses intuitionistic logic.
See also
External links
- Constructive analysis @ Wikipedia
