Smooth infinitesimal analysis

Smooth infinitesimal analysis is a type of mathematics that helps us understand how things change over time. It's a bit like making a movie. Imagine a movie with no cuts. It's like one long shot — you can see every single thing that happens over time, in detail.

In smooth infinitesimal analysis, we use special equations to work out how something changes over time. For example, we could use it to figure out how fast a car is going, or how quickly the temperature changes in a room. It's like taking a lot of very small pictures (like frames in a movie) that show what's happening over time. By looking at each picture separately, we can figure out how the thing changes over time.