Types of theorem

Abstract

In elementary mathematics we frequently assume the existence of a solution to a specific problem. For example, we assume the fundamental theorem of algebra, first proved by Gauss, that every polynomial equation of degree n (in the complex variable z) with complex coefficients has at least one root ∈ ℂ. (An extension of this theorem is that the equation has exactly n roots.) Such a theorem, whose proof is beyond the scope of this book, is called an existence theorem.