A Nonstandard Proof of the Fundamental Theorem of Algebra

ematical logic is analyzing the relationship between mathematical symbols and the objects they represent. This area of study, model theory, shows that for any consistent theory there are many models, or universes, that can be used as interpretations for its symbols. Real analysis, for example, is a theory that has an intended model: the collection of all real numbers, defined as sets of rational numbers, Dedekind cuts. This is a set-theoretic construction devised to provide a formal model. We don't usually think of reals this way, we simply assume that they satisfy the axioms of a complete ordered