I was always taught that 0^0 was equal to 1. Most textbooks I have seen say that it equals 1, and my TI-89 agrees. However, one of my textbooks says it is undefined, and a Google search shows that some other people say so as well. So what is it: 1, undefined, or something else? Is my textbook wrong or is my calculator?
I thought it equalled one, but it makes sense if it’s undefined. I’d go with the textbook or a math teacher/professor for the honest truth, though. As for the TI-89 saying it equals one, well… the unfortunate side-effect of such wonderful machines is that people think they’re right all the time. The trick is knowing when they’re wrong. I had a TI-85, and I remember it giving me an answer for an expression that shouldn’t have one (I think it was inverse sine or something that only works between -1 and 1, but I can’t remember ;)).
The limit of X^0 as X->0 is 1. (2^0=1, x^0=1, so 0^0=1)
The limit of 0^X as X->0 is 0. (0^2=0, 0^1=0, so 0^0=0)
So it’s undefined. Or you need to choose one depending on the circumstances.
By the way my HP-32sII calculator says “Invalid.”
See the sci.math FAQ for 0^0. The result has been argued-about and depends on mathematical context … but the FAQ concludes that most mathematicians view 0^0=1 as the most useful convention to adopt, as it stops 0^0 being a special case in many circumstances (for instance, the binomial theorem).