Archive for May, 2007

Subtraction Without Borrowing

Sunday, May 27th, 2007

I have written a procedure for dynamic subtraction, in which borrowing is replaced by dynamic addition and the subtraction that has to be done is much simpler: it is done within each place-value column, in any order; that is, subtracting the single-digit numbers in each column is completely independent of anything you do in any of the other columns. You can read more about it iin the following sites:

  1. Simplified Procedure
  2. Original (light) Procedure
  3. PDF download of this original version
  4. Detailed Explanation (download a PDF file)
  1. Subtraction Without Borrowing (my article)

Math and Precision

Friday, May 25th, 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.

What Is Math?

Wednesday, May 23rd, 2007

Math is the study of patterns and relationships.
Math explores the world, real and imaginary, by searching for, discovering and studying patterns and relationships. To do so, math employs logic, the art of reasoning. In turns, science, the study of figuring things out, which in turns employs math.