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Algebra Lessons of Life

Quick Links to Sub-Sections
  • Unbuttoning What Has Been Buttoned
  • Measuring It Up with Axioms
  • Performing the Natural Function
  • For the Algebra-Shy (Some Tips)
  • Undressing the Integers

    Then I advanced to the integers, the rationals, and the irrationals--still a part of the discussion on the number system. At this point I realized that many of the concepts and ideas that we have today are simply human conventions, fruits of our imaginations, merely mental constructs. We use our imagination, and accept our fantasies as true if only to give meaning to existence.

    I discovered that when early mathematicians realized that the set of natural numbers could not satisfy an operation such as 1 - 2, they invented the negative numbers. So rose a whole new set of numbers called integers. The negative numbers are those numbers that exist before and beyond nothingness (or 0). Because of the integers, operations like 1 - 2 now have meaning or solutions. I mused myself into believing that human beings behave this way: when we are confronted with an experience that seem meaningless and insignificant, we always try to create ways to give meaning, even if it is merely mental and not necessarily empirical or factual. Say for example, God. Perhaps Voltaire was right in saying that if God did not exist, Man would have to invent him. After all, Man was successful in inventing the integers.

    I learned more about life when I trudged onwards through the rationals and the irrationals. My additional learning came in the humorous and double-meaning words used in the definitions of the rational and irrational numbers. The rational numbers are those that can be expressed as a ratio between two integers while the irrationals are decimal numbers that neither repeat nor terminate. I was thinking of the workers in the factories and offices. Their salary, position, and chances of advancement are always a ratio of two or more factors. It could be gender, education, race, religion, color, the quality of work, the amount of work, the paying capacity of the employer, etc. When I reflected on the irrationals as non-repeating, non-terminating decimals, I discovered that humans who act irrationally behave similarly--they are unpredictable and follow no logical pattern. Isn't that a great way to live? To be unpredictable? It is often helpful to be irrational sometimes, if only to affirm our rationality.

    Next page: Fondling the Polynomials




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