>>12746851
because that's how the real numbers are defined, and they're defined this way because it reflects what we want and expect of them. we want the derivative to be EXACTLY the slope, we want the integral to be EXACTLY the area, not something "infinitesimally" close to it. the archimedean property and standard definition of limit gives you precisely this. feel free to invent your own algebraic structure though, it's not like anyone's stopping you.