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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



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