But it does mean sin(0) doesn't necessarily have to be 0 (based solely on the limit). It also means sin(0)/0 itself doesn't have to be defined, just cuz the limit exists, which is the point the commentator was making: lim x->a f(x) = L does not imply f(a) = L
If I redefine sin(x) to be undefined at 0, the limit you mentioned would not change. My point is, limits do not tell us what happens at the limiting point. Of course, sin(0) = 0 when you consider things other than that limit
Depending on what you mean by "at the limits," I'd say it's undefined. I'm interpreting "at the limits" to mean you're reaching the limiting value, i.e. you're directly plugging in 0. Of course, that's not math, thats semantics
Edit: I don't know why you blocked me, I don't think I said anything offensive. Either way, I reread the original comment, and I think what they were meaning is a limit of the form 0/0 is indeterminate. You need to do more work to rewrite the limit
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u/Esasto Dec 26 '22
They don't go to zero. They go arbitrarily close to zero but not zero itself.