*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## Defining Infinity

Although students are typically taught that "one cannot divide by 0," it can be argued that 0 (read as "one divided by infinity"). How is this possible? Observe the following progression.

Note that as the denominator, or the divisor, becomes larger, the value of the fraction (or the "quotient") becomes smaller. What happens if the denominators become very large?

0.0000001 One can see that as the denominator becomes extremely large, the fraction values approach 0. Indeed, if one thinks of infinity as "ultimately large," one can see that the value of the fraction will likewise be "ultimately small," or 0. Hence, one informal (but useful) way to define infinity is "the number that 1 can be divided by to get 0." Actually, there is no need to use the number 1 as the numerator here; any number divided by infinity will produce 0.

Using algebra, one can come up with another definition of infinity. By transforming...

This section contains 1,286 words(approx. 5 pages at 300 words per page) |