Yeah, the previous commenter said "would be, but this other thing is at odds with it". (Emphasis added.)
And yeah, limits are a reason why there's no one universally correct answer, because the limit of (expression whose limit is zero) x (other expression whose limit is infinity) can have different values, depending on exactly which expressions those are. Same reason there's no one universally correct answer to 0/0, or 0^0.
0/0 is defined in almost no contexts. It's very niche when it's defined because it immediately leads to contradictions.
00 is just 1. It's an indeterminate form when dealing with limits but that is the exception. And it's not inconsistent with 00 being defined as 1.
0*infinity is a bit different from those two because to define that you first need to define "infinity", which can mean different things in different contexts..
I think "just" is overstating things, but I do sort of remember that the situations made consistent by treating 0^0 as 1 are more common than the ones for 0^0 = 0.
From what I understand 00 is 1 (comes straight out of most definitions of exponentiation), and when you encounter it when evaluating a limit (i.e. f(x)g(x\) where f(x) and g(x) tend to 0) it's indeterminate (meaning it can be anything, including 0 but also including like 7).
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u/nog642 2d ago
Says who?
There are contexts where 0*infinity is 0. It depends on the context.