I find it a bit disappointing that the article considers only limits that would justify "0^0 = 0" and "0^0 = 1". In fact, the termin "0^0" as a limit can reach any value - the same way as "0/0" can reach any value.
Im stressing this because back in school, I really thought that although 0^0 is undetermined, it can only reach exactly 0 or 1, but nothing else. This is of course wrong, but no teacher was able to tell me why. For some time I even thought I found a new theorem and tried to prove it. Later, I told some math guru about this, he thought about a minute, and told me two functions f(x) and g(x) whose limit is each 0, but for which the limit of f(x)/g(x) is 2 (or any other value, if you adjust f(x) and g(x) accordingly).
Having said that, in most cases "0^0 = 1" is a useful convention, especially in a purely algebraic context when polynomials are involved.
Im stressing this because back in school, I really thought that although 0^0 is undetermined, it can only reach exactly 0 or 1, but nothing else. This is of course wrong, but no teacher was able to tell me why. For some time I even thought I found a new theorem and tried to prove it. Later, I told some math guru about this, he thought about a minute, and told me two functions f(x) and g(x) whose limit is each 0, but for which the limit of f(x)/g(x) is 2 (or any other value, if you adjust f(x) and g(x) accordingly).
Having said that, in most cases "0^0 = 1" is a useful convention, especially in a purely algebraic context when polynomials are involved.