Saturday, May 26, 2007
Math is perfectly precise. It has to be. Math cannot depend on our ability to draw a straight line, calculate some result or on whether or not we can perform any other mathematical task. Mathematicians have recognized that, no matter how hard anyone tries, it is impossible to achieve, let alone maintain, the precision level math requires. So the mathematical system, which generations of mathematicians developed, accepts our imperfect capabilities and overcomes the drawbacks by maintaining a simple principle. We must be as precise as we can under the given circumstances and do our best to avoid ambiguities. Once we do that, our imprecise mathematical communications can represent perfectly precise mathematical thoughts.