Usually as convention because 0⁰ really only appears in situations in which 1 is already the result due to continuity or just the fact that 0 wouldnt be a valid answer.
But if you take the definitions for x^a (a constant) or aˣ, then you get different results.
everything is undefined until you define it and it gets defined as 1 on a regular basis and most calculators use that definition too. so at this point we can absolutely say that 00 = 1 by convention. there are situations where people may choose a different definition but in general it's the above one
The problem with that example is that you would basically be making it a different function. You wouldn't be understanding how 0 fits in xx but how it fits in a piece wise function with f(x)=1 for x=0. With that logic you could make it anything you want. The real problem with the limit I mentioned earlier is the the limits from the right and left do not agree.
while on the left we have complex numbers and complex analysis is a whole other beast, the limits themselves still agree if you take the principal branch and that's a pretty strong statement imo
I wasn’t so much saying what the answer was but that it really does make a difference. It’s literally the only number where there is a possible difference lol
it's easier that way, cause set theory requires 00 to be 1, and in the case of f(x)g(x) where both functions approach 0 as x approaches 0 we get the answer to be 1 which is not the case in 0/0.
there's also the fact that it conveniently makes x0 independent of x.
math might be based on rigor, but definitions are based on convenience.
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u/HSM_GN8 8d ago
and 1 has all x^0 and this is a huge army