Tag Archives: definitions

Fun with ‘definitions’ in algebra

WARNING:  use the following definitions with great caution. A number phrase is a mathematical phrase which does not express a complete thought. An arithmetic expression is any grammatically sensible expression made up of numbers and (possibly) arithmetic operations (like addition, division, taking the absolute value, etc). Notice that it only has to be grammatically sensible; an undefined expression like 5/0 is… Read More »

Twelve definitions of a square

How does mathematics define a math concept? Definitions of concepts in mathematics are different from definitions of concepts in other discipline or subject area. A definition of a concept in mathematics give a list of properties of that concept. A mathematics object will only be an example of that concept if it fits ALL those requirements, not… Read More »

The heart of mathematics

Axioms, theorems, proofs, definitions, methods, are just some of the sacred words in mathematics. These words command respect and create awe  especially to mathematicians but deliver shock to many students. P.R. Halmos argued that not even one of these sacred words is the heart of mathematics. Then, what is? Problem solving. Solving problems is at… Read More »

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