Undefined FractionsDate: 02/19/2002 at 01:47:35 From: Sandy Morris Subject: Undefined numbers My students always ask, Why is a fraction with a denominator of zero called "undefined"? None of my explanations seem to satisfy the kids. Any ideas? Date: 02/19/2002 at 02:39:12 From: Doctor Jeremiah Subject: Re: Undefined numbers Hi Sandy, A fraction bar is a division symbol, so you are really dividing the top number by the bottom number. But you can't divide by zero, so zero cannot be the bottom number. The reason you can't divide by zero is that no one has bothered to define what it means (thats why it undefined). There is no definition, so dividing by zero has no answer. We could define it to mean something, but we would have to be very careful not to contradict any other math laws along the way. If you define division by zero to mean the same thing as division by any other number, then you can do things like making the number 2 equal to the number 1: False Proofs, Classic Fallacies http://www.mathforum.org/dr.math/faq/faq.false.proof.html So we need to come up with a definition of what it means to divide by zero that is not the same as what division means for every other number. And it would be confusing if division meant two different things (especially in algebra where you have a variable that you don't know the value of!). So to avoid the confusion of having division mean two things, we just don't have a definition for division by zero at all. See the Dr. Math FAQ: Dividing by 0 http://mathforum.org/dr.math/faq/faq.divideby0.html Does that help? - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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