Powers of Infinity ```Name: Ronak S. Status: student Age: N/A Location: N/A Country: N/A Date: 8/6/2004 ``` Question: Why is it that (infinity^0) still remains infinite, when theory tells us that any number raised to 0 is 1? If so how can the above conjecture be proved? Replies: Ronak, The quantity (infinity^0) is what mathematicians call an "indeterminate form". It is not "infinite" as you suggest. It is grouped in a class of mathematical expressions that are not defined and require other tools and ways to investigate situations that lead to these indeterminate forms. Other examples of indeterminate forms include (0/0), (0^0), (1^infinity). Here is a web site that has some elementary details about the definition of indeterminate forms and their evaluations: http://www.sosmath.com/calculus/indforms/intro/intro.html Regards, Todd Clark, Office of Science U.S. Department of Energy Ronak, Infinity is not a number. Infinity is a limit. When you use limits, unexpected things can happen. It is possible for infinity^0 to be infinite. It is possible for infinity^0 to be zero. It is not actually defined. A simpler example appears with division. What is infinity divided by infinity? Most people would say it equals one. (infinity)x(infinity)=(infinity), so (infinity)=(infinity)/(infinity). Depending on how you figure it out, you can get infinity divided by infinity to equal just about anything. Dr. Ken Mellendorf Physics Instructor Illinois Central College Click here to return to the Mathematics Archives

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