/sci/ - Science & Math

>>11107557
>>11107079
Not quite an integral, what I'm trying to get at and where this all stems from is my professor telling me there's no such thing as a derivative or integral for the graph of a series since it's not continuous, it's just points defined at the integers.
Yeah, that's true, but the way my (admittedly naive) brain sees it, I don't know why we can't use a limiting process such that there is a point defined at every real number, like the dirichlet function. Then, since there are infinitely many points, the line would essentially be made continuous (I think)

like with this graph of a series, obviously there's a... curve that it follows, similar in form to the natural log or square root. What I'm thinking is, why can't we just sample more and more points to the point where it's a continuous graph? With it being discrete, there is no way to take a derivative or integral of the series, even though there is clearly a rate of change between the points and an area bounded by the envelope of the curve. I'm aware of discrete differences, but I don't know much about them