Tricki

Think axiomatically even about concrete objects

Quick description

There are many mathematical definitions that are slightly artificial: consider for example the definition of the ordered pair , or the definition of the number . The point of these definitions is not the definitions themselves but the fact that they establish the consistency of certain properties. In proofs, it is almost always better to use the important properties of a definition than to argue directly from the definition. Even when a concrete definition arises naturally and specifies a unique object, it can still be better to focus on characteristic properties and use those.