Scholars frequently organize definitions into five categories: Persuasive, Precising, Theoretical, Lexical, and Stipulative. The last two are of interest to the mathematics teacher and student. A common name for a lexical definition is an extracted definition because it is extracted from common actual usage. Extracted definitions have a truth value—they can be true or false.
As we begin an examination of my vision of twenty-first century mathematics, as it should be, we must establish some fundamentals. Let’s get started. This is important stuff. One of the things we do in mathematics is use deductive reasoning to study relations and operations on mathematical objects. As you read mathematics it will help