Definitions may be either precise or imprecise. The mathematician may define the words that he uses precisely; in his further discussion he then adheres rigorously to the defined meaning of each word. (But for example, the definition of function, the definition of metric space, the definition of topology etc. did take substantial time to evolve…once agreed upon all mathematical community adheres to the definition and hence, math is an exact science in that sense !) We also have standard definitions of fundamental physical quantities, example one kilogram. One kilogram is the mass of as standard object (as defined in SI system of units), the prototype kilogram that is kept in Paris. Similarly, the gram is defined rigorously and precisely as 1/1000 the mass of the kilogram.
On the other hand, the words that are used in describing nature, which is itself quite complex/complicated, may not be capable of precise definition. In giving a definition for such a word the effort is made to describe the “accepted usage.”
Cheers,
Nalin Pithwa
MScMathematics 