(a 2 - b 2) = (a - b)(a + b) for the other side, this can be written as: Now, factoring by a, and using the identity Questions I had were: How can you divide two by zero? Which number, when multiplied by zero, gives you 2?ĭividing by Zero Can Get You into Trouble! If we persist in retaining such errata in our educational texts, an unwitting or unscrupulous person could utilize the result to show that 1 = 2 as follows:įor any finite a. Although both the author and editor insist on this computational outcome, they nonetheless somehow decline to continue the Simplex calculation based on this result, contrary to the logic of their conclusion. A typographical error? Confusion? Willful sin?Ī telephone call bringing the obvious error to the attention of the publisher for correction in future editions was met with an astonishing return call from the editor of the text still insisting that Nay, even educators! These errors can frequently be found as well in prestigious texts published by mainstream publishers.Ī Common Fallacy Reading the 10 th edition of a book on Management Science (Taylor, 2010), I found the author dividing 2 by zero in a Linear Programming Simplex tableau performing a column ratio test, with the stated conclusion, 2 ÃÂ The same errors are commonly committed by seasoned practitioners. It is not simply a problem of ignorance by young novices who have often been mangled. Another fallacy is that the square root of a positive number yields two distinct results. Are we mortals hesitant to admit to our finite nature? Such lighthearted commentary reflects an underlying awkwardness in the manipulation of mathematical expressions where the notions of zero and infinity present themselves. A like uneasiness occurs in confronting infinity, whose proper use first rests on a careful definition of what is finite.
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W should appreciate the grandeur of the achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by Greek antiquity.Ĭulturally, our discomfort with the concepts of zero (and infinite) is reflected in such humor as 2 plus 0 still equals 2, even for large values, and popular retorts of similar tone. But its very simplicity and the great ease, which it has lent to computations put our arithmetic in the first rank of useful inventions. Introduction It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value a profound and important idea which appears so simple to us now that we ignore its true merit.
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Trigonometric Functions and Measuring Angles.Vectors and Numbers: Two Distinct Representations of Numbers.Is 1 a Number or Just a "Unit" for Counting?.Origin of the Common Fallacy: Dividing by Zero.
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Act of Dividing by Zero Is a Meaningless Operation: Forget Its Result.A Sample of the Grown-ups' Arguments Insisting on Dividing by Zero.Dividing by Zero Can Get You into Trouble!." Ln" or " Tan" If the first appearance of the word/phrase is not what you are looking for, try F ind Next. Enter a word or phrase in the dialogue box, e.g. To search the site, try Edit | Find in page.