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## HP 48g Series Calculators - What 0^0 Evaluates To

Issue:
According to a textbook in analysis, 0^0 has no answer that is defined. But my HP 48 answers 1, is that correct?
Solution
The justification that we use comes from the Notices of the American Mathematical Society, September 1991, volume 38, number 7. The section (pages 778 - 785) is entitled "Computers and Mathematics" while the article is called "Crimes and Misdemeanors in the Computer Algebra Trade." The significant part is on page 781:
"If a system transforms x^0 to 1, then, for consistency between the algebra and arithmetic, the system should also transform 0^0 to 1. Kahan [1] and Graham, Knuth, and Patashnik [2] give different persuasive reasons why 0^0 should ordinarily simplify to 1 even in a system that does only arithmetic."
The references are as follows:
[1] Kahan, W. (1987), "Branch Cuts for Complex Elementary Functions or Much Ado about Nothing's Sign Bit," The State of the Art in Numerical Analysis, editors A. Iserles and M. J. D. Powell, Clarendon Press, Oxford, pp. 165--212
[2] Graham, R. L., Knuth, D. E., and Patashnik, O. (1989), Concrete Mathematics, Addison-Wesley Publishing Company, p. 162
There is a response from the Internet newsgroup sci.math. This information is located in their FAQ, which is constantly changing. Read the latest articles from the sci.math newsgroup to find out who currently has their FAQ.

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