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I was recently obsessing over a slightly related topic, which is why the line tangent to point given a neighborhood of that point on a quadratic curve is the midpoint of its derivative on the same interval. It’s now apparent to me that is possibly the most obvious statement you can make it math, but it’s how I came to really understand the delta epsilon situation
What’s fascinating is the radius of the neighborhood, meaning we take a point and make it a midpoint on some interval, Iirc it must be monotonic but not necessarily continuous
As you take this interval and shrink it to zero, the radius becomes a ghost of its former self, yet still of itself. Being nonzero, it Leaves the reals and becomes a new infinitesmal quantity, nonzero but still a quantity, and it is this quantity that we use to obtain the slope
The smallest slice of time With which time can be measured
