Ronny Peine <[EMAIL PROTECTED]> writes: | Hi, | | Kai Henningsen wrote: | > [EMAIL PROTECTED] (Robert Dewar) wrote on 07.03.05 in <[EMAIL PROTECTED]>: | > | >>Ronny Peine wrote: | >> | >> | >>>Sorry for this, maybe i should sleep :) (It's 2 o'clock here) | >>>But as i know of 0^0 is defined as 1 in every lecture i had so far. | >> | >>Were these math classes, or CS classes. | > Let's just say that this didn't happen in any of the German math | > classes I ever took, school or uni. This is in fact a classic | > example of this type of behaviour. | > | >>Generally when you have a situation like this, where the value of | >>the function is different depending on how you approach the limit, | >>you prefer to simply say that the function is undefined at that | >>point. | > And that's how it was always taught to me. | | Well yes, in the general case this is the right way. But for some | special cases a definition is used to simplify mathematical sentences | as it is done for 0^0 = 1 or gcd(0,0,...,0) = 0. See for example: | http://mathworld.wolfram.com/ExponentLaws.html
For _integer_ exponentiation function, pretty much everybody agrees on the convention 0^0 = 1. The issue is radically different for *real* exponentiation. -- Gaby
