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- Existence_theorem abstract "In mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s) ..', or more generally 'for all x, y, ... there exist(s) ...'. That is, in more formal terms of symbolic logic, it is a theorem with a prenex normal form involving the existential quantifier. Many such theorems will not do so explicitly, as usually stated in standard mathematical language. For example, the statement that the sine function is continuous; or any theorem written in big O notation. The quantification can be found in the definitions of the concepts used.A controversy that goes back to the early twentieth century concerns the issue of purely theoretic existence theorems, i.e., theorems depending on non-constructive foundational material such as the axiom of infinity, the axiom of choice, or the law of excluded middle. Such theorems provide no indication as to how to exhibit, or construct, the object whose existence is claimed. From a constructivist viewpoint, by admitting them mathematics loses its concrete applicability. The opposing viewpoint is that abstract methods are far-reaching, in a way that numerical analysis cannot be.".
- Existence_theorem wikiPageID "251177".
- Existence_theorem wikiPageLength "4235".
- Existence_theorem wikiPageOutDegree "25".
- Existence_theorem wikiPageRevisionID "687461910".
- Existence_theorem wikiPageWikiLink Algorithm.
- Existence_theorem wikiPageWikiLink Axiom_of_choice.
- Existence_theorem wikiPageWikiLink Axiom_of_infinity.
- Existence_theorem wikiPageWikiLink Big_O_notation.
- Existence_theorem wikiPageWikiLink Category:Mathematical_theorems.
- Existence_theorem wikiPageWikiLink Constructive_proof.
- Existence_theorem wikiPageWikiLink Constructivism_(mathematics).
- Existence_theorem wikiPageWikiLink Continuous_function.
- Existence_theorem wikiPageWikiLink Errett_Bishop.
- Existence_theorem wikiPageWikiLink Existential_quantification.
- Existence_theorem wikiPageWikiLink First-order_logic.
- Existence_theorem wikiPageWikiLink Intuitionistic_logic.
- Existence_theorem wikiPageWikiLink John_Forbes_Nash,_Jr..
- Existence_theorem wikiPageWikiLink Law_of_excluded_middle.
- Existence_theorem wikiPageWikiLink Mathematics.
- Existence_theorem wikiPageWikiLink Modulus_of_continuity.
- Existence_theorem wikiPageWikiLink Nash_equilibrium.
- Existence_theorem wikiPageWikiLink Numerical_analysis.
- Existence_theorem wikiPageWikiLink Prenex_normal_form.
- Existence_theorem wikiPageWikiLink Sine.
- Existence_theorem wikiPageWikiLink Type_theory.
- Existence_theorem wikiPageWikiLink Uniqueness_theorem.
- Existence_theorem wikiPageWikiLinkText "''pure existence theorem''".
- Existence_theorem wikiPageWikiLinkText "Existence theorem".
- Existence_theorem wikiPageWikiLinkText "Existence theorem#'Pure' existence results".
- Existence_theorem wikiPageWikiLinkText "Existence".
- Existence_theorem wikiPageWikiLinkText "exist".
- Existence_theorem wikiPageWikiLinkText "existence proof".
- Existence_theorem wikiPageWikiLinkText "existence proofs".
- Existence_theorem wikiPageWikiLinkText "existence theorem".
- Existence_theorem wikiPageWikiLinkText "existence".
- Existence_theorem wikiPageWikiLinkText "existence-theorem".
- Existence_theorem wikiPageWikiLinkText "nonconstructive methods".
- Existence_theorem wikiPageWikiLinkText "there exists".
- Existence_theorem wikiPageUsesTemplate Template:Math.
- Existence_theorem wikiPageUsesTemplate Template:Reflist.
- Existence_theorem subject Category:Mathematical_theorems.
- Existence_theorem hypernym Theorem.
- Existence_theorem type Theorem.
- Existence_theorem comment "In mathematics, an existence theorem is a theorem with a statement beginning 'there exist(s) ..', or more generally 'for all x, y, ... there exist(s) ...'. That is, in more formal terms of symbolic logic, it is a theorem with a prenex normal form involving the existential quantifier. Many such theorems will not do so explicitly, as usually stated in standard mathematical language. For example, the statement that the sine function is continuous; or any theorem written in big O notation.".
- Existence_theorem label "Existence theorem".
- Existence_theorem sameAs Q2694495.
- Existence_theorem sameAs Teorema_dexistxc3xa8ncia.
- Existence_theorem sameAs Teorema_de_existencia.
- Existence_theorem sameAs Thxc3xa9orxc3xa8me_dexistence.
- Existence_theorem sameAs 存在定理.
- Existence_theorem sameAs Existentiestelling.
- Existence_theorem sameAs m.01l8mr.
- Existence_theorem sameAs Теорема_существования.
- Existence_theorem sameAs Q2694495.
- Existence_theorem sameAs 存在性定理.
- Existence_theorem wasDerivedFrom Existence_theorem?oldid=687461910.
- Existence_theorem isPrimaryTopicOf Existence_theorem.