existential theorem

An existential theorem is a theoremMathworldPlanetmath which exists.

In general, there are two ways to prove an existential theorem. The most convincing method is a constructive proofMathworldPlanetmath, and another common method is an existential proof. The reason that a constructive proof is most convincing is that, after reading such a proof, readers can actually get their hands on the mathematical in question. In some cases, however, constructing the mathematical is difficult, if not impossible. In this case, an existential proof may be the only method for proving an existential theorem. An example of this is the primitive element theorem.

Title existential theorem
Canonical name ExistentialTheorem
Date of creation 2013-03-22 17:08:57
Last modified on 2013-03-22 17:08:57
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 5
Author Wkbj79 (1863)
Entry type Definition
Classification msc 03F07
Classification msc 00A35
Synonym existence theorem
Related topic TechniquesInMathematicalProofs