How can one lone particular point have a rate of change?
In: Mathematics
This is actually a very important question and the very question that led to a lot of conflict in the math community for many decades regarding if calculus is valid math or means anything. Can even argue that its been a debate lasting literal millennia if you include things like Zeno’s paradox into the debate.
The entire notion of an “instantaneous rate” is a huge paradox if you think about the meaning of those words. It makes absolutely no sense. But we could make rates just less than instantaneous, just not instantaneous itself. To resolve the problem (which was no small feat, it took quite literally over a hundred years to come up with a rigorous answer), we invented the limit and a rigorous look at calculus through the means of a limit. Even then, defining new things to get math to work itself can be thought of as a stretch, though this is how all math works.
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