existential theoremExistentialTheorem2007-05-24 11:31:362007-05-24 12:49:21Definition\usepackage{amssymb}
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An \emph{existential theorem} is a theorem which \PMlinkescapetext{states that a certain mathematical object or property} exists.
In general, there are two ways to prove an existential theorem. The most convincing method is a constructive proof, 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 \PMlinkescapetext{object or property} in question. In some cases, however, constructing the mathematical \PMlinkescapetext{object or property} is difficult, if not impossible. In this case, an existential proof may be the only \PMlinkescapetext{feasible} method for proving an existential theorem. An example of this is the primitive element theorem.