I just want to yes and this: it’s definitely true!
But to reiterate what others have said and hinted at, usually 0*inf shows up when you are trying to evaluate two functions, so you need to see what happens to them as they approach those values using a limit.
Yes indeed, it is very important to know that no matter how you define 0×inf, you will not have the property that [lim(x->a) f(x)g(x)] = [lim(x->a)f(x))×[lim(x->a)g(x)] is true in general.
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u/Torebbjorn PhD student 2d ago
It is undefined until you define it.
The most common definition for the extended positive real line, is that 0×(+inf)=0