In this case, as bucket content aproaches 0 drops, 1 drop becomes infinitely more, at least in calculus.
Limits in calculus:
"When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity" For example, the reciprocal function, f ( x ) = 1/x tends to infinity as x tends to 0.
You think it's possible for a bucket to contain a negative amount of water?
I should note that the product of zero and infinity being an indeterminate form is actually a result about the product of an infinitesimal (of small but indefinite magnitude) and an infinite value. If when you say "zero", you actually mean "zero", there is no ambiguity: zero is more infinitesimal than any infinite value is infinite, and the product of zero with anything, including an infinitely large value, is zero.
> You think it's possible for a bucket to contain a negative amount of water?
Irrelevant, the discontinuity occurs at 0 not a negative number.
The limit of f(X) = (X-2)/(X-2) as X approaches 2 is 1, that doesn’t mean the function has a defined value at 2. Limits seem easy because most students really don’t understand limits and thus misuse them.
Quantum physics tells us all particles are waves, so it’s possible that the amount of water will be negative in some point in time, as long as the average value is not negative. ;-)
Are you trying to make a point? The indeterminate forms are statements about limits. Those limits are statements about the possible range of certain operations on infinitesimal and infinite values. It's perfectly valid to multiply those values. And when zero is one of the multiplicands, it's also the product.
You might want to think about why two times infinity is not an indeterminate form.
If you extend your field to include infinity (e.g. the extended reals, or the extended positive reals), only then is it valid to multiply by infinity. One of the rules in such a system is that when infinity is one of the multiplicands, it's also the product. This gives us conflicting results for zero times infinity, therefore 0*∞ is an indeterminate form.
Limits in calculus: "When a real function can be expressed as a fraction whose denominator tends to zero, the output of the function becomes arbitrarily large, and is said to "tend to infinity" For example, the reciprocal function, f ( x ) = 1/x tends to infinity as x tends to 0.
Source: https://en.m.wikipedia.org/wiki/Division_by_zero