Once a formal system is given, one can define the set of theorems which can be proved inside the formal system. This set consists of all wffs for which there is a proof. Thus all axioms are considered theorems. Unlike the grammar for wffs, there is no guarantee that there will be a decision procedure for deciding whether a given wff is a theorem or not. The notion of theorem just defined should not be confused with theorems about the formal system , which, in order to avoid confusion, are usually called metatheorems .
Longer essays may also contain an introductory page that defines words and phrases of the essay's topic. Most academic institutions require that all substantial facts, quotations, and other porting material in an essay be referenced in a bibliography or works cited page at the end of the text. This scholarly convention helps others (whether teachers or fellow scholars) to understand the basis of facts and quotations the author uses to support the essay's argument and helps readers evaluate to what extent the argument is supported by evidence, and to evaluate the quality of that evidence. The academic essay tests the student's ability to present their thoughts in an organized way and is designed to test their intellectual capabilities.