Is 0^0 defined or not?

Boops · 2004-01-03T08:13:07

My HP48GX calculator sais it's 1 Maple sais it's 1. But at school I learned it's undefined, and so sais my TI40x calculator. However, since Maple is made by mathematicians (I hope so ), who like defenitions and should shudder to program something that's mathematically incorrect, why did they say 0^0 = 1? Trying some things myself, I found that lim_x-->0 x^x = 1, as well as lim_x-->0 -x^-x lim_x-->0 -x^x lim_x-->0 x^-x lim_x-->0 x^0 But the only limitthat becomes 0 instead of 1 is: lim_x-->0 0^x So is that the only one limit that sais the opposite of all the other ones, and is that why they say it's undefined, but because all others say it's 1, they defined it as 1 in Maple? Anyway, personally I'd like if 0^0 was 1, it would make life so much easier EDIT: Hmm I just found this: http://home.att.net/~numericana/answer/algebra.htm, look at the second topic, some guy there is claiming that 0^0=1. Is he right, or is he going to be flamed by any mathematician that sees him? [edited by - Boops on January 1, 2004 6:13:26 PM]