Do Theorems Admit Exceptions? Solid Findings in Mathematics Education on Empirical Proof Schemes

摘要

One of the goals of teaching mathematics is to commu-nicate the purpose and nature of mathematical proof. Jahnke (2008) pointed out that, in everyday thinking, the domain of objects to which a general statement refers is not completely and definitely determined. Thus the very notion of a "universally valid statement" is not as obvi-ous as i might seem. The phenomenon of a statement with an indefinite domain of reference can also be found in the history of mathematics when authors speak of "theorems that admit exceptions".